Zeros of polynomials: matching equation to zeros

WEBVTT
Kind: captions
Language: en

00:00:00.130 --> 00:00:04.740
- A polynomial P has zeros when
X is equal to negative four,

00:00:04.740 --> 00:00:05.950
X is equal to three,

00:00:05.950 --> 00:00:09.020
and X is equal to one-eighth.

00:00:09.020 --> 00:00:11.830
What could be the equation of P?

00:00:11.830 --> 00:00:14.280
So pause this video and
think about it on your own

00:00:14.280 --> 00:00:16.030
before we work through it together.

00:00:17.150 --> 00:00:18.140
All right.

00:00:18.140 --> 00:00:20.540
So the fact that we have
zeros at these values,

00:00:20.540 --> 00:00:22.066
that means that P of X,

00:00:22.066 --> 00:00:25.610
when X is equal to one of
these values is equal to zero.

00:00:25.610 --> 00:00:28.190
So P of negative four is equal to zero,

00:00:28.190 --> 00:00:29.560
P of three is equal to zero,

00:00:29.560 --> 00:00:32.160
and P of one-eighth is equal to zero.

00:00:32.160 --> 00:00:34.100
And before I even look at these choices,

00:00:34.100 --> 00:00:36.450
I could think about
constructing a polynomial for

00:00:36.450 --> 00:00:37.860
which that is true.

00:00:37.860 --> 00:00:41.910
That's going to be true if I
can express this polynomial

00:00:41.910 --> 00:00:45.030
as the product of expressions
where each of these

00:00:45.030 --> 00:00:47.610
would make each of those
expressions equal to zero.

00:00:47.610 --> 00:00:49.670
So what's an expression that would be zero

00:00:49.670 --> 00:00:51.880
when X is equal to negative four?

00:00:51.880 --> 00:00:54.420
Well the expression X plus four,

00:00:54.420 --> 00:00:57.740
this is equal to zero when
X is equal to negative four,

00:00:57.740 --> 00:00:59.190
so I like that.

00:00:59.190 --> 00:01:01.530
What would be an expression
that would be equal to zero

00:01:01.530 --> 00:01:03.320
when X is equal to three?

00:01:03.320 --> 00:01:06.400
Well what about the
expression X minus three?

00:01:06.400 --> 00:01:07.930
If X is equal to three,

00:01:07.930 --> 00:01:09.350
then this is going to
equal to be equal zero.

00:01:09.350 --> 00:01:11.490
Zero times anything is
going to be equal to zero.

00:01:11.490 --> 00:01:13.800
So P of three would be zero in this case.

00:01:13.800 --> 00:01:16.780
And then what is an expression
that would be equal to zero

00:01:16.780 --> 00:01:18.630
when X is equal to one-eighth?

00:01:18.630 --> 00:01:21.930
Well that would be X minus one-eighth.

00:01:21.930 --> 00:01:22.763
Now tho--

00:01:22.763 --> 00:01:23.810
these aren't the only expressions.

00:01:23.810 --> 00:01:26.570
You could multiply them
by constants and still

00:01:26.570 --> 00:01:29.500
the principles that I just
talked about would be true.

00:01:29.500 --> 00:01:31.330
But our polynomial would
look something like this.

00:01:31.330 --> 00:01:32.163
You could try it out.

00:01:32.163 --> 00:01:33.597
If X is equal to negative fou--

00:01:33.597 --> 00:01:34.430
(chuckles)

00:01:34.430 --> 00:01:35.660
if X is equal to negative four,

00:01:35.660 --> 00:01:37.330
well then this first expression is zero.

00:01:37.330 --> 00:01:40.108
Zero times something
times something is zero.

00:01:40.108 --> 00:01:42.180
Same thing for X equals three.

00:01:42.180 --> 00:01:43.370
If this right over--

00:01:43.370 --> 00:01:44.690
If X equals three,

00:01:44.690 --> 00:01:46.770
then X minus three is equal to zero,

00:01:46.770 --> 00:01:49.280
and then zero times something
times something is zero.

00:01:49.280 --> 00:01:50.920
And then if X is equal to one-eighth,

00:01:50.920 --> 00:01:52.930
this expression's going
to be equal to zero.

00:01:52.930 --> 00:01:54.470
Zero times something times something

00:01:54.470 --> 00:01:56.090
is going to be equal to zero.

00:01:56.090 --> 00:01:59.260
So which of these choices look like that?

00:01:59.260 --> 00:02:00.240
So let's see.

00:02:00.240 --> 00:02:01.280
X plus

00:02:01.280 --> 00:02:02.160
four,

00:02:02.160 --> 00:02:05.020
I actually see that in choices

00:02:05.020 --> 00:02:06.110
B,

00:02:06.110 --> 00:02:08.980
and I see that in choices D.

00:02:08.980 --> 00:02:11.670
Choice C has X minus four there.

00:02:11.670 --> 00:02:14.050
So that would have a
zero at X equals four.

00:02:14.050 --> 00:02:15.780
If X equals four, this first--

00:02:15.780 --> 00:02:16.910
this first expression--

00:02:16.910 --> 00:02:18.650
this first part of the expression

00:02:18.650 --> 00:02:20.160
would be equal to zero.

00:02:20.160 --> 00:02:22.100
But we care about that happening when

00:02:22.100 --> 00:02:23.670
X is equal to negative four.

00:02:23.670 --> 00:02:25.400
So I would actually rule out C,

00:02:25.400 --> 00:02:27.920
and then for the same
reason I would rule out A.

00:02:27.920 --> 00:02:29.800
So we're between B and D,

00:02:29.800 --> 00:02:31.330
and now let's see.

00:02:31.330 --> 00:02:33.190
Which of these have an
X minus three in them.

00:02:33.190 --> 00:02:34.630
Well I see an X minus three here.

00:02:34.630 --> 00:02:36.550
I see an X minus three there.

00:02:36.550 --> 00:02:37.730
So I like the--

00:02:37.730 --> 00:02:39.610
I still like B and D.

00:02:39.610 --> 00:02:41.600
I'll put another check
mark right over there.

00:02:41.600 --> 00:02:44.380
And then last but not least,

00:02:44.380 --> 00:02:46.500
which of these would be equal to zero when

00:02:46.500 --> 00:02:48.610
X is equal to one-eighth?

00:02:48.610 --> 00:02:49.550
Well, let's see.

00:02:49.550 --> 00:02:51.790
If I do one-eighth times one-eighth here

00:02:51.790 --> 00:02:53.710
I'm gonna get one-sixty-fourth for

00:02:53.710 --> 00:02:55.200
this part of the expression.

00:02:55.200 --> 00:02:58.510
And so that's not going
to be equal to zero.

00:02:58.510 --> 00:02:59.970
And these other two
things aren't going to be

00:02:59.970 --> 00:03:02.130
equal to zero when X
is equal to one-eighth,

00:03:02.130 --> 00:03:04.340
so this one is not looking so good,

00:03:04.340 --> 00:03:06.110
but let's verify this one.

00:03:06.110 --> 00:03:07.410
This has--

00:03:07.410 --> 00:03:08.460
If X is equal to one-eighth,

00:03:08.460 --> 00:03:11.530
we have eight times
one-eighth which is one,

00:03:11.530 --> 00:03:12.500
minus one.

00:03:12.500 --> 00:03:13.930
That is going to be equal to zero,

00:03:13.930 --> 00:03:15.970
so this one checks out.

00:03:15.970 --> 00:03:17.500
And you might be thinking hey!

00:03:17.500 --> 00:03:19.940
This last polynomial looks
a little bit different

00:03:19.940 --> 00:03:21.760
than this polynomial that I wrote up here

00:03:21.760 --> 00:03:24.650
when I just tried to come up
with a polynomial for which

00:03:24.650 --> 00:03:26.350
this would be true.

00:03:26.350 --> 00:03:27.400
And as I mentioned,

00:03:27.400 --> 00:03:29.530
you could take this and
multiply it by constants

00:03:29.530 --> 00:03:31.600
and it would still be true.
So if you just take this,

00:03:31.600 --> 00:03:33.800
and if we were to multiply it by eight,

00:03:33.800 --> 00:03:35.670
you would get P of X down here,

00:03:35.670 --> 00:03:38.330
because if we were to
multiply this times eight,

00:03:38.330 --> 00:03:40.330
which wouldn't change the zeros,

00:03:40.330 --> 00:03:43.030
well then if you distribute this eight,

00:03:43.030 --> 00:03:47.080
this last expression would
become eight X minus one.

00:03:47.080 --> 00:03:49.243
Which is exactly what we have down here.


Zeros of polynomials: matching equation to graph

WEBVTT
Kind: captions
Language: en

00:00:00.140 --> 00:00:01.410
- [Instructor] We are asked, what could

00:00:01.410 --> 00:00:02.990
be the equation of p?

00:00:02.990 --> 00:00:06.120
And we have graph of our
polynomial p right over here,

00:00:06.120 --> 00:00:07.365
you could view this as the graph

00:00:07.365 --> 00:00:10.860
of y is equal to p of x.

00:00:10.860 --> 00:00:14.310
So pause this video and see
if you can figure that out.

00:00:14.310 --> 00:00:16.000
All right, now let's
work on this together,

00:00:16.000 --> 00:00:18.245
and you can see that all
the choices have p of x,

00:00:18.245 --> 00:00:19.943
in factored form where it's very easy

00:00:19.943 --> 00:00:22.468
to identify the zeros or the x values

00:00:22.468 --> 00:00:25.280
that would make our
polynomial equal to zero.

00:00:25.280 --> 00:00:26.760
And we could also look at this graph

00:00:26.760 --> 00:00:29.180
and we can see what the zeros are.

00:00:29.180 --> 00:00:31.534
This is where we're going
to intersect the x-axis,

00:00:31.534 --> 00:00:33.910
also known as the x-intercepts.

00:00:33.910 --> 00:00:37.630
So you can see when x is
equal to negative four,

00:00:37.630 --> 00:00:42.630
we have a zero because our
polynomial is zero there.

00:00:42.820 --> 00:00:46.040
So we know p of negative
four is equal to zero.

00:00:46.040 --> 00:00:49.210
We also know that p of, looks like 1 1/2,

00:00:49.210 --> 00:00:50.300
or I could say 3/2.

00:00:50.300 --> 00:00:53.480
p of 3/2 is equal to zero,

00:00:53.480 --> 00:00:57.478
and we also know that p
of three is equal to zero.

00:00:57.478 --> 00:01:00.970
So let's look for an
expression where that is true.

00:01:00.970 --> 00:01:02.328
And because it's in factored form,

00:01:02.328 --> 00:01:05.879
each of the parts of the product

00:01:05.879 --> 00:01:08.235
will probably make our polynomial zero

00:01:08.235 --> 00:01:10.520
for one of these zeroes.

00:01:10.520 --> 00:01:12.632
So let's see if, if in
order for our polynomial

00:01:12.632 --> 00:01:15.760
to be equal to zero when x
is equal to negative four,

00:01:15.760 --> 00:01:16.814
we probably want to have a term

00:01:16.814 --> 00:01:19.810
that has an x plus four in it.

00:01:19.810 --> 00:01:21.380
Or we want to have a, I should say,

00:01:21.380 --> 00:01:24.160
a product that has an x plus four in it.

00:01:24.160 --> 00:01:25.152
Because x plus four is equal

00:01:25.152 --> 00:01:28.198
to zero when x is equal to negative four.

00:01:28.198 --> 00:01:29.902
Well we have an x plus four there,

00:01:29.902 --> 00:01:32.010
and we have an x plus four there.

00:01:32.010 --> 00:01:34.720
So I'm liking choices B and D so far.

00:01:34.720 --> 00:01:39.720
Now for this second root, we have p of 3/2

00:01:39.880 --> 00:01:41.194
is equal to zero so I would look

00:01:41.194 --> 00:01:46.194
for something like x
minus 3/2 in our product.

00:01:46.980 --> 00:01:49.590
I don't see an x minus 3/2 here,

00:01:49.590 --> 00:01:51.070
but as we've mentioned in other videos

00:01:51.070 --> 00:01:53.580
you can also multiply
these times constants.

00:01:53.580 --> 00:01:54.413
So if I were to multiply,

00:01:54.413 --> 00:01:56.490
let's see to get rid
of this fraction here,

00:01:56.490 --> 00:01:59.270
if I multiply by two this
would be the same thing as,

00:01:59.270 --> 00:02:01.060
let me scroll down a little bit,

00:02:01.060 --> 00:02:04.320
same thing as two x minus three.

00:02:04.320 --> 00:02:05.470
And you could test that out,

00:02:05.470 --> 00:02:08.393
two x minus three is equal to
zero when x is equal to 3/2.

00:02:09.280 --> 00:02:14.040
And let's see, we have a two x
minus three right over there.

00:02:14.040 --> 00:02:15.793
So choice D is looking awfully good,

00:02:15.793 --> 00:02:18.097
but let's just verify
it with this last one.

00:02:18.097 --> 00:02:20.720
For p of three to be equal to zero,

00:02:20.720 --> 00:02:22.204
we could have an expression

00:02:22.204 --> 00:02:25.260
like x minus three in the product

00:02:25.260 --> 00:02:27.880
because this is equal to zero
when x is equal to three,

00:02:27.880 --> 00:02:30.550
and we indeed have that right over there.

00:02:30.550 --> 00:02:34.440
So choice D is looking very good.

00:02:34.440 --> 00:02:36.225
When x is equal to negative four,

00:02:36.225 --> 00:02:39.559
this part of our product is equal

00:02:39.559 --> 00:02:43.010
to zero which makes the
whole thing equal to zero.

00:02:43.010 --> 00:02:47.660
When x is equal to 3/2,
two x minus three is equal

00:02:47.660 --> 00:02:50.110
to zero which makes the
entire product equal to zero.

00:02:50.110 --> 00:02:52.910
And when x minus, and when
an x is equal to three,

00:02:52.910 --> 00:02:54.990
it makes x minus three equal to zero.

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Zero times something, times something

00:02:56.473 --> 00:02:58.913
is going to be equal to zero.


LearnStorm Classroom Celebrations

WEBVTT
Kind: captions
Language: en

00:00:00.200 --> 00:00:02.072
- [Woman] Okay, you ready
to check our progress?

00:00:02.072 --> 00:00:03.190
- [Children] Yeah.

00:00:03.190 --> 00:00:04.272
- [Woman] All right, here we go.

00:00:04.272 --> 00:00:06.635
(children cheering)

00:00:06.635 --> 00:00:08.384
- [Children] Go, go, go, go, go.

00:00:08.384 --> 00:00:11.017
- [Children] 70, 70, 70.

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80, 80, 80.

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- [Children] Not yet, not yet.

00:00:14.325 --> 00:00:16.393
(children cheering)

00:00:16.393 --> 00:00:18.771
(children stomping)

00:00:18.771 --> 00:00:21.771
(children cheering)

00:00:26.124 --> 00:00:29.223
(students clapping)

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(children cheering)


Polynomial division introduction

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:01.700
- [Instructor] We're already familiar

00:00:01.700 --> 00:00:04.500
with the idea of a polynomial

00:00:04.500 --> 00:00:07.650
and we've spent some
time adding polynomials,

00:00:07.650 --> 00:00:09.140
subtracting polynomials,

00:00:09.140 --> 00:00:10.580
and multiplying polynomials,

00:00:10.580 --> 00:00:12.070
and factoring polynomials.

00:00:12.070 --> 00:00:13.790
And what we're going to
think about in this video

00:00:13.790 --> 00:00:15.870
and really start to
think about in this video

00:00:15.870 --> 00:00:20.020
is the idea of polynomial division.

00:00:20.020 --> 00:00:22.140
So, for example.

00:00:22.140 --> 00:00:24.110
If I had the polynomial,

00:00:24.110 --> 00:00:26.290
and this would be a quadratic polynomial,

00:00:26.290 --> 00:00:31.270
let's say x squared plus three x

00:00:32.110 --> 00:00:36.830
plus two, and I wanted to divide it

00:00:36.830 --> 00:00:39.470
by x plus one.

00:00:39.470 --> 00:00:40.610
Pause this video and think about

00:00:40.610 --> 00:00:42.120
what would that be?

00:00:42.120 --> 00:00:44.950
What would I have to
multiply x plus one by

00:00:44.950 --> 00:00:47.653
to get x squared plus three x plus two?

00:00:48.530 --> 00:00:50.140
Well, one way to approach it is

00:00:50.140 --> 00:00:51.760
we could try to factor x squared

00:00:51.760 --> 00:00:52.880
plus three x plus two

00:00:52.880 --> 00:00:55.970
and we've done that
multiple times in our lives.

00:00:55.970 --> 00:00:58.200
We think about well, what
two numbers add up to three

00:00:58.200 --> 00:01:00.480
and if I were to multiply them I get two.

00:01:00.480 --> 00:01:01.730
And the one that might jump,

00:01:01.730 --> 00:01:03.390
or the ones that might jump out at you

00:01:03.390 --> 00:01:04.710
are two and one.

00:01:04.710 --> 00:01:06.530
And so we could express x squared

00:01:06.530 --> 00:01:10.260
plus three x plus two as x plus two

00:01:10.260 --> 00:01:13.590
times x plus one, and then all of that

00:01:13.590 --> 00:01:17.600
is going to be over x plus one.

00:01:17.600 --> 00:01:19.600
And so, if you were to take x plus two

00:01:19.600 --> 00:01:21.810
times x plus one, and then divide that

00:01:21.810 --> 00:01:24.580
by x plus one, what is that going to be?

00:01:24.580 --> 00:01:26.350
Well, you're just going to be left with

00:01:26.350 --> 00:01:27.910
an x plus two.

00:01:27.910 --> 00:01:29.590
This is going, you don't
have to put parentheses,

00:01:29.590 --> 00:01:31.600
this is going to be an x plus two.

00:01:31.600 --> 00:01:33.770
And if we want to be really
mathematically precise

00:01:33.770 --> 00:01:35.410
we would say hey, this would be true

00:01:35.410 --> 00:01:38.140
as long as x does not equal,

00:01:38.140 --> 00:01:40.990
x does not equal negative one,

00:01:40.990 --> 00:01:42.640
because if x equals negative one

00:01:42.640 --> 00:01:44.960
in this expression or this expression

00:01:44.960 --> 00:01:46.560
we're gonna be dividing by zero.

00:01:46.560 --> 00:01:48.030
And we know that leads to all sorts

00:01:48.030 --> 00:01:49.900
of mathematical problems.

00:01:49.900 --> 00:01:52.160
But as we see, for any other x

00:01:52.160 --> 00:01:54.920
as long as we're not
dividing by zero here,

00:01:54.920 --> 00:01:56.280
this expression is going to be

00:01:56.280 --> 00:01:57.590
the same thing as x plus two,

00:01:57.590 --> 00:01:59.340
and that's because x plus two

00:01:59.340 --> 00:02:01.990
times x plus one is equal to what we have

00:02:01.990 --> 00:02:04.050
in this numerator here.

00:02:04.050 --> 00:02:08.000
Now, as we go deeper
into polynomial division,

00:02:08.000 --> 00:02:09.860
we're going to approach things

00:02:09.860 --> 00:02:11.210
that aren't as easy to do

00:02:11.210 --> 00:02:12.720
just purely through factoring.

00:02:12.720 --> 00:02:14.410
And that's where we're
gonna have a technique

00:02:14.410 --> 00:02:17.570
called polynomial long division.

00:02:17.570 --> 00:02:19.250
Polynomial long division,

00:02:19.250 --> 00:02:23.470
sometimes known as
algebraic long division.

00:02:23.470 --> 00:02:25.790
And if it sounds familiar,

00:02:25.790 --> 00:02:27.750
because you first learned
about long division

00:02:27.750 --> 00:02:28.680
in fourth or fifth grade,

00:02:28.680 --> 00:02:31.070
it's because it's a very similar process

00:02:31.070 --> 00:02:34.260
where you would take your x plus one

00:02:34.260 --> 00:02:36.020
and you would try to divide it

00:02:36.020 --> 00:02:41.020
into your x squared plus three x plus two.

00:02:42.100 --> 00:02:42.950
And you do.

00:02:42.950 --> 00:02:45.180
Something very, and I'm
gonna do a very quick example

00:02:45.180 --> 00:02:46.360
right over here, but we're gonna do

00:02:46.360 --> 00:02:47.810
much more detailed examples

00:02:47.810 --> 00:02:49.390
in future videos, but you look

00:02:49.390 --> 00:02:50.570
at the highest degree terms.

00:02:50.570 --> 00:02:52.280
You say okay, I have a first degree term,

00:02:52.280 --> 00:02:53.710
I have a second degree term here.

00:02:53.710 --> 00:02:56.100
How many times is x going to x squared?

00:02:56.100 --> 00:02:58.170
Well, it goes x times.

00:02:58.170 --> 00:03:00.850
So you put the x in
the first degree column

00:03:00.850 --> 00:03:03.620
and then you multiply
your x times x plus one.

00:03:03.620 --> 00:03:05.660
X times x is x squared.

00:03:05.660 --> 00:03:07.220
X times one is x.

00:03:07.220 --> 00:03:10.320
And then you subtract this from that.

00:03:10.320 --> 00:03:12.000
So you might already start to see

00:03:12.000 --> 00:03:13.980
some parallels with the long division

00:03:13.980 --> 00:03:16.610
that you first learned
in school many years ago.

00:03:16.610 --> 00:03:18.660
So when you do that, these cancel out,

00:03:18.660 --> 00:03:20.080
three x minus x.

00:03:20.080 --> 00:03:22.280
We are left with a two x.

00:03:22.280 --> 00:03:23.900
And then you bring down that two.

00:03:23.900 --> 00:03:25.207
So two x plus two.

00:03:25.207 --> 00:03:27.130
And you say how many times does x

00:03:27.130 --> 00:03:28.550
go into two x?

00:03:28.550 --> 00:03:30.350
Well, it goes two times.

00:03:30.350 --> 00:03:32.000
So you have a plus two here.

00:03:32.000 --> 00:03:33.180
Two times x plus one.

00:03:33.180 --> 00:03:35.700
Two times x is two x.

00:03:35.700 --> 00:03:37.440
Two times one is two.

00:03:37.440 --> 00:03:39.950
You can subtract these and then

00:03:39.950 --> 00:03:42.490
you are going to be left with nothing.

00:03:42.490 --> 00:03:43.800
Two minus two is zero.

00:03:43.800 --> 00:03:46.300
Two x minus two x is zero.

00:03:46.300 --> 00:03:48.610
So in this situation it divided

00:03:48.610 --> 00:03:51.570
cleanly into it and we got x plus two,

00:03:51.570 --> 00:03:54.570
which is exactly what we had over there.

00:03:54.570 --> 00:03:55.910
Now, an interesting scenario

00:03:55.910 --> 00:03:57.430
that we are also going to approach

00:03:57.430 --> 00:03:58.890
in the next few videos,

00:03:58.890 --> 00:04:01.350
is what if things don't divide cleanly?

00:04:01.350 --> 00:04:03.700
For example, if I were to add one

00:04:03.700 --> 00:04:06.170
to x squared plus three x plus two,

00:04:06.170 --> 00:04:11.170
I would get x squared
plus three x plus three.

00:04:11.190 --> 00:04:12.770
And if I were to try to divide that

00:04:12.770 --> 00:04:15.510
by x plus one, well, it's not going

00:04:15.510 --> 00:04:16.870
to divide cleanly anymore.

00:04:16.870 --> 00:04:18.870
You could it either approach.

00:04:18.870 --> 00:04:20.370
One way to think about it, if we know

00:04:20.370 --> 00:04:22.450
we can factor x squared
plus three x plus two

00:04:22.450 --> 00:04:25.330
is say hey, this is the same thing as

00:04:25.330 --> 00:04:30.330
x squared plus three x plus two plus one,

00:04:30.380 --> 00:04:34.320
and then all of that's
going to be over x plus one.

00:04:34.320 --> 00:04:35.590
And then you could say hey,

00:04:35.590 --> 00:04:36.810
this is the same thing

00:04:36.810 --> 00:04:41.020
as x squared plus three x plus two

00:04:41.020 --> 00:04:43.350
over x plus one,

00:04:43.350 --> 00:04:44.820
over x plus one,

00:04:44.820 --> 00:04:47.050
plus one over x plus one.

00:04:47.050 --> 00:04:51.040
Plus one over x plus one.

00:04:51.040 --> 00:04:52.530
And we already figured out

00:04:52.530 --> 00:04:54.640
that this expression on the left,

00:04:54.640 --> 00:04:57.440
as long as x does not equal negative one,

00:04:57.440 --> 00:05:00.080
this is going to be equal to x plus two.

00:05:00.080 --> 00:05:02.000
So this is going to be
equal to x plus two,

00:05:02.000 --> 00:05:03.250
but then we have that one

00:05:03.250 --> 00:05:05.770
that we were able to
divide x plus one into,

00:05:05.770 --> 00:05:08.540
so we're just left with
the one over x plus one.

00:05:08.540 --> 00:05:10.610
And we'll study that in a lot more detail

00:05:10.610 --> 00:05:11.443
in other videos.

00:05:11.443 --> 00:05:12.800
What does this remainder mean

00:05:12.800 --> 00:05:13.950
and how do we calculate it

00:05:13.950 --> 00:05:15.880
if we can't factor part of what we have

00:05:15.880 --> 00:05:16.820
in the numerator?

00:05:16.820 --> 00:05:19.160
And as we do our polynomial long division

00:05:19.160 --> 00:05:21.150
we'll see that the remainder will show up

00:05:21.150 --> 00:05:24.030
at the end when we are done dividing.

00:05:24.030 --> 00:05:26.153
We'll see those examples in future videos.


Zeros of polynomials introduction

WEBVTT
Kind: captions
Language: en

00:00:00.270 --> 00:00:03.730
- [Instructor] Let's say that
we have a polynomial, p of x,

00:00:03.730 --> 00:00:05.160
and we can factor it,

00:00:05.160 --> 00:00:10.160
and we can put it in the form
x minus one times x plus two

00:00:11.260 --> 00:00:16.260
times x minus three times x plus four.

00:00:16.400 --> 00:00:18.550
And what we are concerned with

00:00:18.550 --> 00:00:22.590
are the zeros of this polynomial,

00:00:22.590 --> 00:00:26.750
and you might say, "What
is a zero of a polynomial?"

00:00:26.750 --> 00:00:28.700
Well, those are the x-values

00:00:28.700 --> 00:00:32.180
that are going to make the
polynomial equal to zero.

00:00:32.180 --> 00:00:33.820
So another way to think about it is,

00:00:33.820 --> 00:00:38.820
for what x-values is p of x
going to be equal to zero,

00:00:39.210 --> 00:00:41.130
or another way you can think about it is,

00:00:41.130 --> 00:00:43.650
for what x-values is this expression

00:00:43.650 --> 00:00:45.180
going to be equal to zero.

00:00:45.180 --> 00:00:50.150
So for what x-values is x
minus one times x plus two

00:00:50.150 --> 00:00:54.870
times x minus three times x plus four,

00:00:54.870 --> 00:00:57.180
going to be equal to zero.

00:00:57.180 --> 00:00:58.680
I encourage you to pause this video,

00:00:58.680 --> 00:00:59.720
and think about that a little bit

00:00:59.720 --> 00:01:01.920
before we work through it together.

00:01:01.920 --> 00:01:04.820
Well the key realization here
is if you have the product

00:01:04.820 --> 00:01:06.520
of a bunch of expressions,

00:01:06.520 --> 00:01:08.600
if any one of them is equal to zero,

00:01:08.600 --> 00:01:10.060
it doesn't matter what the others are,

00:01:10.060 --> 00:01:11.720
because zero times anything else

00:01:11.720 --> 00:01:13.420
is going to be equal to zero.

00:01:13.420 --> 00:01:17.130
So the fancy term for that
is the zero product property.

00:01:17.130 --> 00:01:19.870
But all it says is, hey,
if you can find an x-value

00:01:19.870 --> 00:01:23.600
that makes any one of these
expressions equal to zero,

00:01:23.600 --> 00:01:26.190
well that's going to make the
entire expression going to be,

00:01:26.190 --> 00:01:29.260
it's going to make the entire
expression equal to zero.

00:01:29.260 --> 00:01:32.700
So, the zeros of this polynomial
are gonna be the x-values

00:01:32.700 --> 00:01:35.770
that could make x minus one equal to zero.

00:01:35.770 --> 00:01:37.390
So x minus one equals zero.

00:01:37.390 --> 00:01:40.350
Well we know what x-value
would make that happen,

00:01:40.350 --> 00:01:42.882
if x is equal to one, if you
add one to both sides here,

00:01:42.882 --> 00:01:47.882
x equals one, so x equals one
is a zero of this polynomial.

00:01:47.930 --> 00:01:51.620
Another way to say that is
p of one when x equals one,

00:01:51.620 --> 00:01:53.360
that whole polynomial is
going to be equal to zero.

00:01:53.360 --> 00:01:54.580
How do I know that?

00:01:54.580 --> 00:01:57.110
Well if I put a one in, right over here,

00:01:57.110 --> 00:02:00.350
this expression right
over here, x minus one,

00:02:00.350 --> 00:02:02.480
that is going to be equal to zero.

00:02:02.480 --> 00:02:04.270
So you're gonna have zero
times a bunch of other stuff

00:02:04.270 --> 00:02:06.470
which is going to be equal to zero.

00:02:06.470 --> 00:02:08.240
And so by the same idea,

00:02:08.240 --> 00:02:10.430
we can figure out what
the other zeros are.

00:02:10.430 --> 00:02:14.710
What would make this part equal to zero?

00:02:14.710 --> 00:02:17.944
What x-value would make
x plus two equal to zero?

00:02:17.944 --> 00:02:22.500
Well, x equals negative
two, x equals negative two,

00:02:22.500 --> 00:02:24.760
would make x plus two equal zero.

00:02:24.760 --> 00:02:28.630
So x equals negative two is
another zero of this polynomial.

00:02:28.630 --> 00:02:30.600
And we could keep going.

00:02:30.600 --> 00:02:33.769
What would make x minus
three equal to zero?

00:02:33.769 --> 00:02:36.439
Well if x is equal to three,

00:02:36.439 --> 00:02:39.320
that would make x minus
three equal to zero,

00:02:39.320 --> 00:02:41.230
and that would then make
the entire expression

00:02:41.230 --> 00:02:42.310
equal to zero.

00:02:42.310 --> 00:02:44.370
And then last but not least,

00:02:44.370 --> 00:02:47.580
what would make x plus four equal to zero?

00:02:47.580 --> 00:02:50.120
Well if x is equal to negative four.

00:02:50.120 --> 00:02:51.010
And just like that

00:02:51.010 --> 00:02:54.760
we have found four zeros
for this polynomial,

00:02:54.760 --> 00:02:57.290
when x equals one the
polynomial's equal to zero,

00:02:57.290 --> 00:02:59.580
when x equals negative two the
polynomial's equal to zero,

00:02:59.580 --> 00:03:02.020
when x equals three the
polynomial's equal to zero,

00:03:02.020 --> 00:03:03.730
and when x equals negative four

00:03:03.730 --> 00:03:05.480
the polynomial's equal to zero.

00:03:05.480 --> 00:03:07.030
And one of the interesting things

00:03:07.030 --> 00:03:09.230
about the zeros of a polynomial

00:03:09.230 --> 00:03:11.370
you could actually use
that to start to sketch out

00:03:11.370 --> 00:03:13.470
what the graph might look like.

00:03:13.470 --> 00:03:16.550
So, for example, we know,
that this polynomial

00:03:16.550 --> 00:03:21.190
is going to take on the
value zero at these zeros.

00:03:21.190 --> 00:03:23.320
So let me just draw a rough
sketch right over here.

00:03:23.320 --> 00:03:28.250
So this is my x-axis, that's
my y-axis, that's my y-axis.

00:03:28.250 --> 00:03:31.050
And so, let's see, at x equals one,

00:03:31.050 --> 00:03:31.940
so let me just do it this way,

00:03:31.940 --> 00:03:36.920
so we have one, two, three, and four.

00:03:36.920 --> 00:03:41.797
Then you have negative one,
negative two, negative three,

00:03:41.797 --> 00:03:44.439
and then last but not
least, negative four.

00:03:44.439 --> 00:03:47.470
We know that this polynomial, p of x,

00:03:47.470 --> 00:03:50.190
is going to be equal to
zero at x equals one.

00:03:50.190 --> 00:03:53.100
So it's going to intersect
the x-axis right there.

00:03:53.100 --> 00:03:56.470
It's going to be equal to
zero at x equals negative two,

00:03:56.470 --> 00:03:58.023
so right over there.

00:03:58.023 --> 00:04:00.840
At x equals three, right over there.

00:04:00.840 --> 00:04:02.800
And x equals negative four.

00:04:02.800 --> 00:04:05.150
Now we don't know exactly
what the graph looks like,

00:04:05.150 --> 00:04:06.150
just based on this.

00:04:06.150 --> 00:04:08.690
We could try out some values
on either side to figure out,

00:04:08.690 --> 00:04:11.570
hey, is it above the
x-axis, or below the x-axis,

00:04:11.570 --> 00:04:13.427
for x-values less than negative four.

00:04:13.427 --> 00:04:15.060
And we can try things out like that

00:04:15.060 --> 00:04:18.290
but we know it intersects
the x-axis at these points.

00:04:18.290 --> 00:04:21.270
So it might look something like this,

00:04:21.270 --> 00:04:22.947
this is a very rough sketch.

00:04:22.947 --> 00:04:26.930
It might look something like this,

00:04:26.930 --> 00:04:30.340
we don't know without doing
a little bit more work.

00:04:30.340 --> 00:04:32.920
But ahead of time, I took a
look at what this looks like,

00:04:32.920 --> 00:04:34.850
I went on to Desmos, and I graphed it,

00:04:34.850 --> 00:04:39.670
and you can see, it looks
exactly as what we would expect.

00:04:39.670 --> 00:04:43.160
The graph of this polynomial
intersects the x-axis

00:04:43.160 --> 00:04:45.930
at x equals negative four,
actually let me color code it,

00:04:45.930 --> 00:04:47.710
x equals negative four,

00:04:47.710 --> 00:04:50.280
and that is that zero right over there,

00:04:50.280 --> 00:04:54.588
x equals negative two,
that's this zero right there,

00:04:54.588 --> 00:04:58.380
x equals one, right over there,

00:04:58.380 --> 00:05:03.380
and then x equals three, right over there.

00:05:03.492 --> 00:05:06.923
In future videos we will
study this in even more depth.


Intro to Economics - Course Trailer

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:04.340
- Welcome to Introduction to Economics.

00:00:04.340 --> 00:00:08.340
You are about to become an
economically-literate person.

00:00:08.340 --> 00:00:10.300
You might not realize
this, but you've always

00:00:10.300 --> 00:00:12.280
been an economic actor.

00:00:12.280 --> 00:00:15.460
When you've decided to spend
your time doing one thing,

00:00:15.460 --> 00:00:18.340
you might have foregone being
able to do other things,

00:00:18.340 --> 00:00:20.190
that's an opportunity cost.

00:00:20.190 --> 00:00:23.020
When you decided to buy something,

00:00:23.020 --> 00:00:25.940
you might ask yourself,
why did I pay that price?

00:00:25.940 --> 00:00:28.840
Would I pay more or less if
there were more of that thing?

00:00:28.840 --> 00:00:30.700
Would I pay more or less
if there were more mes

00:00:30.700 --> 00:00:32.190
who wanted to buy that thing?

00:00:32.190 --> 00:00:33.190
All of a sudden, you're getting

00:00:33.190 --> 00:00:35.860
into the ideas of supply and demand.

00:00:35.860 --> 00:00:37.560
As we go into these lessons, we're going

00:00:37.560 --> 00:00:39.570
to dig a little bit deeper at a little bit

00:00:39.570 --> 00:00:41.780
of math, a little bit of visualizations,

00:00:41.780 --> 00:00:44.740
where we'll see that these
simple but very powerful

00:00:44.740 --> 00:00:49.740
frameworks apply to things
as complex as economies.

00:00:49.960 --> 00:00:53.180
The entire academic field of economics

00:00:53.180 --> 00:00:56.300
is studying how things should be allocated

00:00:56.300 --> 00:00:58.210
when there's not enough for everyone

00:00:58.210 --> 00:01:00.660
to get as much as they want,
that's known as scarcity.

00:01:00.660 --> 00:01:03.230
How do you allocate scarce resources?

00:01:03.230 --> 00:01:05.870
And to do that, you
have to make trade-offs.

00:01:05.870 --> 00:01:08.650
We're also going to learn
about concepts of trade.

00:01:08.650 --> 00:01:09.920
Why is trade good?

00:01:09.920 --> 00:01:11.720
Ideas like comparative advantage,

00:01:11.720 --> 00:01:13.790
but also why trade might not always

00:01:13.790 --> 00:01:15.530
be in everyone's interest.

00:01:15.530 --> 00:01:17.850
And as we go into these
and we study things

00:01:17.850 --> 00:01:20.850
like supply and demand,
perhaps most importantly,

00:01:20.850 --> 00:01:23.740
we're gonna start to learn
to think like an economist,

00:01:23.740 --> 00:01:25.240
where instead of just
thinking about things

00:01:25.240 --> 00:01:28.230
like prices and scarcity,
and supply and demand,

00:01:28.230 --> 00:01:29.690
and everyday language, we're gonna think

00:01:29.690 --> 00:01:30.970
about how do we model them?

00:01:30.970 --> 00:01:32.560
Because once we can model them and think

00:01:32.560 --> 00:01:34.430
about them visually and mathematically,

00:01:34.430 --> 00:01:38.090
we can come to interesting
and rigorous conclusions.

00:01:38.090 --> 00:01:41.130
Economics is sometimes
called the dismal science,

00:01:41.130 --> 00:01:43.270
which some might view
as a bit of an insult

00:01:43.270 --> 00:01:45.380
to the field, but I
view it as a compliment,

00:01:45.380 --> 00:01:47.040
because what's interesting
about economics,

00:01:47.040 --> 00:01:48.940
it has some traits that
make it a little bit more

00:01:48.940 --> 00:01:50.430
like traditional sciences.

00:01:50.430 --> 00:01:52.020
We're going to use some mathematics,

00:01:52.020 --> 00:01:53.840
we're going to do some
diagrams, we're going

00:01:53.840 --> 00:01:56.100
to be thinking
systematically about things.

00:01:56.100 --> 00:01:58.430
But it has another aspect of it

00:01:58.430 --> 00:02:00.260
that is a lot like the humanities.

00:02:00.260 --> 00:02:03.160
We're gonna talk about how humans act,

00:02:03.160 --> 00:02:05.560
and especially how they act in aggregate.

00:02:05.560 --> 00:02:07.110
Even as we look at these models

00:02:07.110 --> 00:02:09.270
and we try to understand
things mathematically,

00:02:09.270 --> 00:02:11.130
we're always going to be asking ourselves,

00:02:11.130 --> 00:02:13.370
well what assumptions
did we make to do that?

00:02:13.370 --> 00:02:15.780
Is that true, are all humans rational

00:02:15.780 --> 00:02:17.230
when they make these decisions?

00:02:17.230 --> 00:02:19.156
Or are there animal
spirits that get worked

00:02:19.156 --> 00:02:21.530
up where we sometimes
do irrational things,

00:02:21.530 --> 00:02:22.960
where as a group, it actually could

00:02:22.960 --> 00:02:24.270
be a little less predictable

00:02:24.270 --> 00:02:27.030
than the mathematical models predict.

00:02:27.030 --> 00:02:30.110
So this is going to be a fun
beginning to our journey.

00:02:30.110 --> 00:02:32.640
And like always, if you're interested

00:02:32.640 --> 00:02:34.660
in this topic and you want to go deeper

00:02:34.660 --> 00:02:37.480
and you want to get practice
with immediate feedback,

00:02:37.480 --> 00:02:41.513
you could look at all of these
lessons at khanacademy.org.


Algebra Foundations - Course Trailer

WEBVTT
Kind: captions
Language: en

00:00:00.250 --> 00:00:02.210
- When you're sitting in a math class

00:00:02.210 --> 00:00:05.480
and the teacher starts writing
some symbols on the board

00:00:05.480 --> 00:00:08.610
that you might not quite
understand just yet,

00:00:08.610 --> 00:00:09.797
it might be tempting to say,

00:00:09.797 --> 00:00:12.207
"Hey, why do I need to lean this?

00:00:12.207 --> 00:00:14.980
"This seems a little bit abstract for me."

00:00:14.980 --> 00:00:16.070
And to answer that,

00:00:16.070 --> 00:00:19.680
I'll tell you a story that one
of my early advisors told me

00:00:19.680 --> 00:00:21.210
when I was just starting Khan Academy.

00:00:21.210 --> 00:00:23.580
This is someone who doesn't
come from engineering,

00:00:23.580 --> 00:00:25.140
doesn't come from science,

00:00:25.140 --> 00:00:27.090
and doesn't come from mathematics.

00:00:27.090 --> 00:00:29.330
He's actually a major restaurateur who has

00:00:29.330 --> 00:00:32.160
a chain of restaurants some
of you might have gone to.

00:00:32.160 --> 00:00:35.730
And he says when he hires people,

00:00:35.730 --> 00:00:38.180
he thinks about whether they
understand algebra or not.

00:00:38.180 --> 00:00:39.020
In fact, in his mind,

00:00:39.020 --> 00:00:41.830
he devices the world into
people who understand algebra

00:00:41.830 --> 00:00:43.620
and people who do not understand algebra.

00:00:43.620 --> 00:00:47.490
And the reason why he told
me he does that is he says

00:00:47.490 --> 00:00:49.430
when people understand algebra,

00:00:49.430 --> 00:00:52.560
it gives him confidence that
they have the critical thinking

00:00:52.560 --> 00:00:54.450
and analytical skills to tackle

00:00:54.450 --> 00:00:57.840
pretty much any problem in any domain.

00:00:57.840 --> 00:01:00.240
And I think that is the practical reason

00:01:00.240 --> 00:01:01.910
why algebra is so powerful.

00:01:01.910 --> 00:01:04.520
It's really going to start to fine-tune

00:01:04.520 --> 00:01:06.960
your critical thinking
skills and your logic.

00:01:06.960 --> 00:01:09.580
And beyond that, it's
frankly just beautiful.

00:01:09.580 --> 00:01:12.330
A lot of the equations
you're going to learn,

00:01:12.330 --> 00:01:14.100
the ways of manipulating equations,

00:01:14.100 --> 00:01:17.210
philosophers, mathematicians
were developing these

00:01:17.210 --> 00:01:18.920
for thousands of years,

00:01:18.920 --> 00:01:21.830
and now you get to understand the outcome

00:01:21.830 --> 00:01:23.540
of their thousands of years

00:01:23.540 --> 00:01:24.720
of hitting a head against the wall

00:01:24.720 --> 00:01:27.300
and coming up with these
beautiful expressions

00:01:27.300 --> 00:01:31.270
that are really the fundamental
truths of the universe.

00:01:31.270 --> 00:01:33.940
So when you go into this algebra journey

00:01:33.940 --> 00:01:35.120
that we're about to start,

00:01:35.120 --> 00:01:36.400
learn the math,

00:01:36.400 --> 00:01:37.850
learn the tools you're about to,

00:01:37.850 --> 00:01:40.000
because it's really a form of expression.

00:01:40.000 --> 00:01:43.600
It's a form, it's a way of representing

00:01:43.600 --> 00:01:47.410
pure ideas in the universe and our minds.

00:01:47.410 --> 00:01:48.720
In these lessons,

00:01:48.720 --> 00:01:50.470
we're going to talk about
some of that history,

00:01:50.470 --> 00:01:52.300
the origins of algebra.

00:01:52.300 --> 00:01:53.600
We're also going to think about

00:01:53.600 --> 00:01:55.810
what is an algebraic expression,

00:01:55.810 --> 00:01:58.320
and what are things like
unknowns and variables?

00:01:58.320 --> 00:02:00.390
And finally, we're going to really start

00:02:00.390 --> 00:02:01.730
to build out our toolkit

00:02:01.730 --> 00:02:03.690
on how do we manipulate these things?

00:02:03.690 --> 00:02:05.840
How do we speak the language of algebra

00:02:05.840 --> 00:02:10.000
and utilize these tools to
solve everyday problems?

00:02:10.000 --> 00:02:11.940
So let's start this adventure together.

00:02:11.940 --> 00:02:13.660
There might be moments where you're

00:02:13.660 --> 00:02:15.430
a little bit unsure of yourself,

00:02:15.430 --> 00:02:17.160
or you're a little bit not sure

00:02:17.160 --> 00:02:18.930
of how one thing leads to another.

00:02:18.930 --> 00:02:20.120
But trust me,

00:02:20.120 --> 00:02:23.330
if you go into the content, pause videos,

00:02:23.330 --> 00:02:25.110
and see if you can
solve things on your own

00:02:25.110 --> 00:02:27.230
before I work through it with you,

00:02:27.230 --> 00:02:29.580
and then make sure again that
you can do it on your own.

00:02:29.580 --> 00:02:32.450
And I encourage you to
go to khanacademy.org

00:02:32.450 --> 00:02:35.410
and practice these same
concepts on the site,

00:02:35.410 --> 00:02:37.000
where you'll get immediate feedback,

00:02:37.000 --> 00:02:39.370
to make sure that you're
understanding them.

00:02:39.370 --> 00:02:41.730
Algebra is going to be a powerful toolkit

00:02:41.730 --> 00:02:43.050
not just for your studies,

00:02:43.050 --> 00:02:44.653
but for your entire life.


Foundations of American Democracy  -  Course Trailer

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:04.140
- Welcome to foundations
of American democracy.

00:00:04.140 --> 00:00:07.370
This is where it all begins.

00:00:07.370 --> 00:00:10.140
You might think it's just
about the United States.

00:00:10.140 --> 00:00:12.350
But here we're going to go much deeper,

00:00:12.350 --> 00:00:14.240
and much further back than that.

00:00:14.240 --> 00:00:16.620
We're gonna go to the original ideas.

00:00:16.620 --> 00:00:18.230
Deep dive into philosophy.

00:00:18.230 --> 00:00:20.200
What are the rights of the individual,

00:00:20.200 --> 00:00:23.600
and what rights are they
willing to give up to a state,

00:00:23.600 --> 00:00:26.210
in order to have those
individual rights protected.

00:00:26.210 --> 00:00:29.240
And this is something that
humanity has struggled with

00:00:29.240 --> 00:00:32.140
for thousands and thousands of years.

00:00:32.140 --> 00:00:35.180
But over those thousands
and thousands of years,

00:00:35.180 --> 00:00:37.790
as for the most part
humanity was controlled

00:00:37.790 --> 00:00:40.180
by kings and emperors,

00:00:40.180 --> 00:00:44.580
little ideas, like democracy,
started to sprout up

00:00:44.580 --> 00:00:47.930
in places like ancient
Greece, and then in Rome,

00:00:47.930 --> 00:00:49.340
and all of these were imperfect,

00:00:49.340 --> 00:00:50.440
and many of us would argue

00:00:50.440 --> 00:00:53.720
that never have they quite
been perfected just yet.

00:00:53.720 --> 00:00:56.010
But really it starts to accelerate

00:00:56.010 --> 00:00:58.780
in this part of our study,

00:00:58.780 --> 00:00:59.670
where we're going to see

00:00:59.670 --> 00:01:01.550
that the enlightenment in Europe

00:01:01.550 --> 00:01:04.910
sprouts these questions
of do we even need kings,

00:01:04.910 --> 00:01:08.070
especially when we just
fought a big war against them.

00:01:08.070 --> 00:01:11.690
Could we create a new type
of governance structure.

00:01:11.690 --> 00:01:13.873
And what you might not realize is

00:01:13.873 --> 00:01:16.460
the United States at its founding

00:01:16.460 --> 00:01:18.460
was really something of an experiment.

00:01:18.460 --> 00:01:22.140
A state, like the United
States, did not exist.

00:01:22.140 --> 00:01:24.750
In fact, in the beginning,
it did not even view itself

00:01:24.750 --> 00:01:28.130
as one state, or one country,
but a collection of countries.

00:01:28.130 --> 00:01:30.420
So as you'll go through this
journey, you're going to see

00:01:30.420 --> 00:01:33.820
this fascinating philosophical deep dive,

00:01:33.820 --> 00:01:38.170
into the ideas of what
makes a government function,

00:01:38.170 --> 00:01:40.250
and what powers should it have,

00:01:40.250 --> 00:01:42.730
and what powers should it not have.

00:01:42.730 --> 00:01:45.820
What powers should go
to the aggregate state,

00:01:45.820 --> 00:01:48.930
the United States, and
what powers should go

00:01:48.930 --> 00:01:52.090
to the individual members,
to the states themselves.

00:01:52.090 --> 00:01:57.090
How does a population protect
themselves from the tyranny

00:01:57.160 --> 00:01:59.770
of a potential king, or
the potential dictator.

00:01:59.770 --> 00:02:02.440
In the coming lessons
we're going to dive deep

00:02:02.440 --> 00:02:05.210
into the ideals of American democracy.

00:02:05.210 --> 00:02:08.400
We're going to learn about the
debates between the groups,

00:02:08.400 --> 00:02:10.740
some of whom thought that
the federal government

00:02:10.740 --> 00:02:13.360
should have more power,
and others who thought

00:02:13.360 --> 00:02:15.350
that the states should have more power.

00:02:15.350 --> 00:02:18.400
And we'll learn how it all played out

00:02:18.400 --> 00:02:20.630
in our actual Constitution.

00:02:20.630 --> 00:02:23.650
What powers are in the hands
of the federal government,

00:02:23.650 --> 00:02:26.170
what powers are in the hands
of the state governments,

00:02:26.170 --> 00:02:28.630
and what powers are in the hands of both.

00:02:28.630 --> 00:02:31.010
So let's start this journey together,

00:02:31.010 --> 00:02:34.580
and to learn more about these ideas,

00:02:34.580 --> 00:02:37.650
and to get practice
with immediate feedback,

00:02:37.650 --> 00:02:41.763
I encourage you to look at these
lessons on KhanAcademy.org.


The Fifth Amendment

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:02.500
- [Kim] Hi, this is Kim from Khan Academy.

00:00:02.500 --> 00:00:03.950
Today we're learning more about

00:00:03.950 --> 00:00:06.710
the takings clause of the Fifth Amendment.

00:00:06.710 --> 00:00:08.210
In another video we'll discuss

00:00:08.210 --> 00:00:10.020
the other clauses of the Fifth Amendment,

00:00:10.020 --> 00:00:12.260
those that deal with self-incrimination

00:00:12.260 --> 00:00:13.700
and due process of law.

00:00:13.700 --> 00:00:15.270
But in this video we're concentrating

00:00:15.270 --> 00:00:18.270
on just the last few words
of the Fifth Amendment

00:00:18.270 --> 00:00:21.870
which forbid the government
from taking private property

00:00:21.870 --> 00:00:25.290
for public use without just compensation.

00:00:25.290 --> 00:00:27.400
To learn more about the takings clause,

00:00:27.400 --> 00:00:29.520
I sought out the help of two experts.

00:00:29.520 --> 00:00:33.160
Richard Epstein is the Lawrence
A Tisch Professor of Law

00:00:33.160 --> 00:00:36.900
and Director of the Classical
Liberal Institute at NYU Law.

00:00:36.900 --> 00:00:39.620
He's also a Senior Fellow
at the Hoover Institution.

00:00:39.620 --> 00:00:43.400
Eduardo Penalver is the
Allan R. Tessler Professor

00:00:43.400 --> 00:00:45.820
and Dean of Cornell Law School.

00:00:45.820 --> 00:00:48.590
So Prof. Epstein can you
give us a little background?

00:00:48.590 --> 00:00:50.830
Just what is the taking clause?

00:00:50.830 --> 00:00:53.200
- [Richard] Well, there's a
rule in Constitutional Law

00:00:53.200 --> 00:00:54.530
that the shorter the provision,

00:00:54.530 --> 00:00:56.730
the more difficult the interpretation.

00:00:56.730 --> 00:00:59.380
And this is a very short petition.

00:00:59.380 --> 00:01:02.157
It says, "nor shall
private property be taken

00:01:02.157 --> 00:01:05.940
"for public use without
just compensation."

00:01:05.940 --> 00:01:08.190
And the first thing to
understand about the clause

00:01:08.190 --> 00:01:10.240
is that it's in the passive voice.

00:01:10.240 --> 00:01:12.450
So it doesn't tell you who's taking it.

00:01:12.450 --> 00:01:15.590
And early on, since this was
the part of the Bill of Rights,

00:01:15.590 --> 00:01:19.160
it was said to apply only to
Congress and not to the states.

00:01:19.160 --> 00:01:23.730
And then after the Civil War,
through the 14th Amendment,

00:01:23.730 --> 00:01:25.580
it was said to apply to the states.

00:01:25.580 --> 00:01:27.047
So now it applies to both the states

00:01:27.047 --> 00:01:29.030
and to the Federal government.

00:01:29.030 --> 00:01:31.210
- [Eduardo] Many constitutions don't have

00:01:31.210 --> 00:01:34.180
an explicit property protection clause,

00:01:34.180 --> 00:01:38.750
but there's a fairly strong norm

00:01:38.750 --> 00:01:41.590
around compensating
owners of private property

00:01:41.590 --> 00:01:44.790
when you, essentially
commandeer their property

00:01:44.790 --> 00:01:45.880
for public purposes.

00:01:45.880 --> 00:01:48.380
And that seems to have
been the motivation.

00:01:48.380 --> 00:01:52.090
It's, the clearest reading of it is that

00:01:52.090 --> 00:01:55.500
it's a provision of the
Constitution that makes clear

00:01:55.500 --> 00:01:59.060
that when the Federal
government takes your property,

00:01:59.060 --> 00:02:02.630
or when the states takes your
property for some public use,

00:02:02.630 --> 00:02:04.560
that they have to make you whole

00:02:04.560 --> 00:02:07.030
by giving you just compensation.

00:02:07.030 --> 00:02:09.500
- [Richard] Private property's
a pretty comprehensive term.

00:02:09.500 --> 00:02:11.630
Everybody understands that it means land

00:02:11.630 --> 00:02:13.190
and the things you build on land.

00:02:13.190 --> 00:02:16.000
They also understand that
it tends to cover chattels,

00:02:16.000 --> 00:02:18.960
that is things like books and baseballs

00:02:18.960 --> 00:02:22.000
that you happen to own and wild animals.

00:02:22.000 --> 00:02:24.730
But it's also, it's
much broader than that.

00:02:24.730 --> 00:02:26.840
It covers all sorts of intangible rights,

00:02:26.840 --> 00:02:29.960
like patents, copyrights, trade secrets.

00:02:29.960 --> 00:02:32.750
These are very complicated
and generally speaking

00:02:32.750 --> 00:02:34.430
the government doesn't have any obligation

00:02:34.430 --> 00:02:35.870
to create a patent,

00:02:35.870 --> 00:02:37.220
but once it gives you the patent

00:02:37.220 --> 00:02:38.870
it just can't take it from you

00:02:38.870 --> 00:02:42.020
because the patent after
conferred, is in fact,

00:02:42.020 --> 00:02:43.730
now a property right.

00:02:43.730 --> 00:02:45.680
And then it also may or may not cover

00:02:45.680 --> 00:02:48.300
other kinds of intangibles like good will

00:02:48.300 --> 00:02:51.200
which is the value
associated with the business,

00:02:51.200 --> 00:02:52.880
knowing that your past customers

00:02:52.880 --> 00:02:55.140
may come back to you in the future.

00:02:55.140 --> 00:02:56.810
- [Eduardo] On the motives of the Framers

00:02:56.810 --> 00:03:01.210
for including this talk about
things like the confiscation,

00:03:01.210 --> 00:03:03.120
mostly of personal property

00:03:03.120 --> 00:03:06.723
during the Revolutionary War
by the British government,

00:03:07.660 --> 00:03:10.380
that was possibly motivation to make clear

00:03:10.380 --> 00:03:12.820
that if in future scenarios

00:03:12.820 --> 00:03:14.630
if the government wanted
to take your property

00:03:14.630 --> 00:03:18.040
it would have to, it would
have to compensate you.

00:03:18.040 --> 00:03:19.560
And I think most historians don't think

00:03:19.560 --> 00:03:22.580
there was a real problem
being addressed by this.

00:03:22.580 --> 00:03:26.240
A problem of uncompensated
taking of property

00:03:26.240 --> 00:03:30.130
by colonial governments
during that period,

00:03:30.130 --> 00:03:32.280
or by the state governments

00:03:32.280 --> 00:03:34.160
during the Articles of Confederation.

00:03:34.160 --> 00:03:35.580
- [Richard] The Framers wanted a system

00:03:35.580 --> 00:03:37.870
of what we call limited government.

00:03:37.870 --> 00:03:40.227
And so the takings clause,
essentially says, is

00:03:40.227 --> 00:03:42.637
"yes, we need your land for a fort,

00:03:42.637 --> 00:03:44.647
"and it's really very important.

00:03:44.647 --> 00:03:46.887
"But if we're gonna take
it and use it for a fort,

00:03:46.887 --> 00:03:50.197
"that's a public use, we're
gonna pay you compensation

00:03:50.197 --> 00:03:51.957
"for the fair market value of the land

00:03:51.957 --> 00:03:53.880
"before the fort was put on."

00:03:53.880 --> 00:03:55.770
And this is in order to make sure

00:03:55.770 --> 00:03:57.960
that you can't pick and
choose your victims,

00:03:57.960 --> 00:04:00.430
and it's a way of assuring
government regularity.

00:04:00.430 --> 00:04:01.620
That's the first.

00:04:01.620 --> 00:04:03.760
Second thing is more economic,

00:04:03.760 --> 00:04:05.800
less apparent at the time of the Framing,

00:04:05.800 --> 00:04:07.880
but pretty apparent today.

00:04:07.880 --> 00:04:09.350
Is if the government can take something

00:04:09.350 --> 00:04:12.550
and not pay you compensation,
it's gonna overtake.

00:04:12.550 --> 00:04:16.700
So your land is worth $100,000 as a farm,

00:04:16.700 --> 00:04:18.760
but if you're gonna use it for a fort

00:04:18.760 --> 00:04:20.750
it's only worth $10,000.

00:04:20.750 --> 00:04:22.800
If you don't have to pay the $100,000,

00:04:22.800 --> 00:04:26.250
well you may take it because
you get $10,000 worth of gain.

00:04:26.250 --> 00:04:28.460
But if you have to pay the
fellow a fair market value

00:04:28.460 --> 00:04:30.950
of the property interest
taking, you won't do it.

00:04:30.950 --> 00:04:33.580
So essentially what it
does is it makes sure,

00:04:33.580 --> 00:04:35.330
or at least improves the odds,

00:04:35.330 --> 00:04:37.120
that when the government
does take property,

00:04:37.120 --> 00:04:39.480
or does regulate, it will in fact

00:04:39.480 --> 00:04:41.440
improve overall social welfare.

00:04:41.440 --> 00:04:45.300
So you have a political function
dealing with singling out

00:04:45.300 --> 00:04:47.210
and you have an economic function

00:04:47.210 --> 00:04:50.240
dealing with the overall
improvement of government behavior

00:04:50.240 --> 00:04:52.170
from an economic point of view.

00:04:52.170 --> 00:04:55.540
- [Kim] Okay, so say I had a piece of land

00:04:55.540 --> 00:04:56.920
and the government decided

00:04:56.920 --> 00:04:59.680
that they wanted it for some purpose.

00:04:59.680 --> 00:05:01.660
What would be the legal process

00:05:01.660 --> 00:05:05.750
for the government to go
about acquiring my land?

00:05:05.750 --> 00:05:08.100
- [Eduardo] Well, the
process for eminent domain

00:05:08.100 --> 00:05:09.540
really varies by state,

00:05:09.540 --> 00:05:11.540
but typically there's some notice

00:05:11.540 --> 00:05:13.130
that the government gives you

00:05:13.130 --> 00:05:15.050
that it intends to take your property.

00:05:15.050 --> 00:05:16.730
The government goes to court

00:05:16.730 --> 00:05:18.510
and gets an order of condemnation

00:05:18.510 --> 00:05:19.990
to take title of the property.

00:05:19.990 --> 00:05:22.100
And then often as a requirement

00:05:22.100 --> 00:05:24.360
that the government bargain with you

00:05:24.360 --> 00:05:26.390
about the value of the property.

00:05:26.390 --> 00:05:28.680
It will tell you what
it thinks the value is,

00:05:28.680 --> 00:05:30.970
the fair market value is
the standard that we use

00:05:30.970 --> 00:05:32.180
for just compensation.

00:05:32.180 --> 00:05:36.270
That's the value that a
willing buyer would pay

00:05:36.270 --> 00:05:39.150
to a willing seller for the land.

00:05:39.150 --> 00:05:42.620
It doesn't include things
like your sentimental value

00:05:42.620 --> 00:05:43.453
or anything like that.

00:05:43.453 --> 00:05:46.250
So it's just the market
value of the property.

00:05:46.250 --> 00:05:48.550
There's some back and forth

00:05:48.550 --> 00:05:49.600
through this required bargaining.

00:05:49.600 --> 00:05:51.580
If the government and the property owner

00:05:51.580 --> 00:05:52.413
can't reach an agreement,

00:05:52.413 --> 00:05:53.770
then the government can go to court

00:05:53.770 --> 00:05:57.520
and get the court to specify
the value of the property

00:05:57.520 --> 00:05:59.200
that would aid in compensation.

00:05:59.200 --> 00:06:03.010
And then the payment is made
and the deed is transferred

00:06:03.010 --> 00:06:05.710
and the government becomes
the owner of the property.

00:06:05.710 --> 00:06:07.370
- [Kim] Interesting, so the government

00:06:07.370 --> 00:06:09.780
has gone through this process
to try to acquire my land.

00:06:09.780 --> 00:06:11.190
What if I'm a real hold-out

00:06:11.190 --> 00:06:14.800
and I just really don't want
the government to get my land?

00:06:14.800 --> 00:06:15.633
What happens then?

00:06:15.633 --> 00:06:17.997
- [Eduardo] Well, you can
litigate various pieces of this,

00:06:17.997 --> 00:06:20.210
and again it depends a
little bit on the state law,

00:06:20.210 --> 00:06:23.390
so some states put more procedural hurdles

00:06:23.390 --> 00:06:24.503
in the way of the government,

00:06:24.503 --> 00:06:27.660
then other states make it
easier for the government.

00:06:27.660 --> 00:06:31.250
But under the Constitution
there are really only two ways

00:06:31.250 --> 00:06:34.120
you can resist the taking of your property

00:06:34.120 --> 00:06:34.953
through eminent domain.

00:06:34.953 --> 00:06:38.770
One is by arguing that the
use that the government plans

00:06:38.770 --> 00:06:40.450
to make of your property doesn't count

00:06:40.450 --> 00:06:42.690
as a legitimate public use.

00:06:42.690 --> 00:06:45.077
Because the clause says,
"nor shall private property

00:06:45.077 --> 00:06:47.650
"be taken for public use
without just compensation."

00:06:47.650 --> 00:06:49.990
And that public use language
has been interpreted

00:06:49.990 --> 00:06:52.780
to be a limitation on the
power of eminent domain.

00:06:52.780 --> 00:06:54.790
And then you can argue, the
second thing you can argue

00:06:54.790 --> 00:06:56.750
is that what the
government is offering you

00:06:56.750 --> 00:07:00.453
in terms of just compensation
is not adequate compensation.

00:07:01.460 --> 00:07:03.400
And you can litigate
those through the courts

00:07:03.400 --> 00:07:06.300
and that can slow the
process down quite a bit.

00:07:06.300 --> 00:07:08.267
Some states make it easier
for the government by saying,

00:07:08.267 --> 00:07:10.737
"well the government can
actually just take title,

00:07:10.737 --> 00:07:12.320
"while you litigate."

00:07:12.320 --> 00:07:16.070
And others make you go, you know,

00:07:17.540 --> 00:07:20.330
allow you to stop the condemnation process

00:07:20.330 --> 00:07:21.630
and litigate in advance.

00:07:21.630 --> 00:07:25.420
But there's often what's
called a quick-take procedure

00:07:25.420 --> 00:07:27.863
which allows the government
to move more quickly

00:07:27.863 --> 00:07:29.910
and put the litigation on the back end.

00:07:29.910 --> 00:07:34.350
But the public use, if the
use is found not to be public,

00:07:34.350 --> 00:07:37.230
what you win is, you got
an actual prohibition

00:07:37.230 --> 00:07:38.910
on the taking itself.

00:07:38.910 --> 00:07:39.840
You keep your property.

00:07:39.840 --> 00:07:42.160
If you win on the just compensation side,

00:07:42.160 --> 00:07:44.623
all you get is more money,
they still take your property.

00:07:44.623 --> 00:07:45.456
(laughs)

00:07:45.456 --> 00:07:47.400
- [Kim] So, you mentioned public use.

00:07:47.400 --> 00:07:49.880
What counts as public use?

00:07:49.880 --> 00:07:52.500
- [Eduardo] Well, under the current law,

00:07:52.500 --> 00:07:55.400
any use that generates a public benefit

00:07:55.400 --> 00:07:57.740
is really a public use.

00:07:57.740 --> 00:08:00.920
So the way the court has put
it is anything the government,

00:08:00.920 --> 00:08:05.040
any purpose the government can pursue

00:08:05.040 --> 00:08:06.580
through any other means,

00:08:06.580 --> 00:08:08.930
it can pursue through eminent domain.

00:08:08.930 --> 00:08:12.330
So, if the government
wants to create jobs,

00:08:12.330 --> 00:08:14.050
or if the government wants to beautify,

00:08:14.050 --> 00:08:18.387
or if the government
wants to remove blight,

00:08:18.387 --> 00:08:21.100
all those things are things
that we think it's legitimate

00:08:21.100 --> 00:08:23.030
for the government to try to do.

00:08:23.030 --> 00:08:25.530
If it can do those things, it can do them

00:08:25.530 --> 00:08:27.630
through the use of the
eminent domain power.

00:08:27.630 --> 00:08:30.270
- [Kim] One thing that
strikes me as interesting

00:08:30.270 --> 00:08:35.270
is just the fact that this
clause is in the Fifth Amendment

00:08:35.540 --> 00:08:40.460
among things like, double
jeopardy or self-incrimination.

00:08:40.460 --> 00:08:42.940
So why do you think the Framers included

00:08:42.940 --> 00:08:45.300
this particular clause here

00:08:45.300 --> 00:08:48.030
as opposed to elsewhere
in the Bill of Rights?

00:08:48.030 --> 00:08:49.390
- [Richard] Well that's a great question

00:08:49.390 --> 00:08:50.950
to which there's no obvious answer,

00:08:50.950 --> 00:08:53.980
but the one clause that
is pretty close to it

00:08:53.980 --> 00:08:56.370
is the due process clause
in the Fifth Amendment

00:08:56.370 --> 00:08:58.797
which says, "nor shall
any person be deprived

00:08:58.797 --> 00:09:01.950
"of life, liberty or property
without due process of law."

00:09:01.950 --> 00:09:05.110
So if you start with the procedural stuff,

00:09:05.110 --> 00:09:07.097
somebody's gonna say,
"well, how do we know

00:09:07.097 --> 00:09:09.340
"that the procedures aren't fair?"

00:09:09.340 --> 00:09:11.500
And if it turns out
that the government uses

00:09:11.500 --> 00:09:15.040
a set of procedures that don't
give you adequate notice,

00:09:15.040 --> 00:09:16.740
you're always going to end up short

00:09:16.740 --> 00:09:19.550
on the amount of compensation
that you're gonna acquire.

00:09:19.550 --> 00:09:22.710
So bad procedures tend
to lead to bad outcomes

00:09:22.710 --> 00:09:25.080
which tend to lead to property being taken

00:09:25.080 --> 00:09:27.180
at less than full market value.

00:09:27.180 --> 00:09:30.120
So what happens is is
therefore very close linkage

00:09:30.120 --> 00:09:34.150
between the procedures used
under the due process clause

00:09:34.150 --> 00:09:37.400
and the substance of protection
that you have under takings.

00:09:37.400 --> 00:09:40.010
- [Kim] Any changes in the interpretation

00:09:40.010 --> 00:09:42.770
of the takings clause by
the Supreme Court over time?

00:09:42.770 --> 00:09:44.470
- [Richard] Well there's been a huge

00:09:44.470 --> 00:09:46.050
kind of switch up and down

00:09:46.050 --> 00:09:48.550
and let me put it the following way.

00:09:48.550 --> 00:09:50.950
In the beginning there
wasn't much of anything

00:09:50.950 --> 00:09:53.480
that was done with respect
to the takings clause.

00:09:53.480 --> 00:09:55.800
The first Federal case to deal with it

00:09:55.800 --> 00:10:00.770
was called Barron against
Baltimore in 1833 or so.

00:10:00.770 --> 00:10:04.590
And it just simply said that
the clause does not allow

00:10:04.590 --> 00:10:08.630
for protection of Mr. Barron
against the city of Baltimore,

00:10:08.630 --> 00:10:10.940
because it only binds
the Federal government,

00:10:10.940 --> 00:10:12.550
it doesn't bind the state.

00:10:12.550 --> 00:10:15.690
After the Civil War, two things happened

00:10:15.690 --> 00:10:17.480
of real distinction.

00:10:17.480 --> 00:10:18.390
The first thing is

00:10:18.390 --> 00:10:21.200
you start getting comprehensive regulation

00:10:21.200 --> 00:10:24.000
of the railroads and the
rates they can charge

00:10:24.000 --> 00:10:25.820
and then public utilities

00:10:25.820 --> 00:10:27.650
and the rates that they can charge.

00:10:27.650 --> 00:10:31.090
And then in 1921 there's a
case called Block v. Hirsch

00:10:31.090 --> 00:10:33.770
and it's a very close
five to four decision.

00:10:33.770 --> 00:10:36.580
But they sustain on the
grounds that it's a war time,

00:10:36.580 --> 00:10:39.420
a temporary two year statue
that limits the rents

00:10:39.420 --> 00:10:41.800
that can be charged in Washington D.C.

00:10:41.800 --> 00:10:42.633
at the end of the first World War.

00:10:42.633 --> 00:10:44.140
- [Eduardo] One of the biggest changes

00:10:44.140 --> 00:10:45.640
in the interpretation
of the takings clause

00:10:45.640 --> 00:10:48.350
was the extension of the
takings clause to govern

00:10:48.350 --> 00:10:50.330
situations in which your property

00:10:50.330 --> 00:10:53.210
was not appropriated by the government.

00:10:53.210 --> 00:10:55.860
So what we called the
Regulatory Takings Doctrine

00:10:55.860 --> 00:10:59.540
which started in, with the case

00:10:59.540 --> 00:11:04.480
of Pennsylvania Coal
versus Mahon in the 1920s

00:11:04.480 --> 00:11:07.000
and then has now become much more,

00:11:07.000 --> 00:11:08.380
it was sort of dormant for a while,

00:11:08.380 --> 00:11:11.193
would become much more
active since the 1980s.

00:11:12.350 --> 00:11:15.070
That's a doctrine that says
if the government regulates

00:11:15.070 --> 00:11:17.840
your use of property excessively,

00:11:17.840 --> 00:11:20.280
then the courts can treat that,

00:11:20.280 --> 00:11:22.810
in effect as a confiscation
of your property

00:11:22.810 --> 00:11:24.860
and require the payment
of just compensation.

00:11:24.860 --> 00:11:27.440
That was a pretty, that's maybe
the most significant change

00:11:27.440 --> 00:11:31.030
in the interpretation of
the clause in its history.

00:11:31.030 --> 00:11:32.680
So there continues to be controversy

00:11:32.680 --> 00:11:34.410
about the public use doctrine.

00:11:34.410 --> 00:11:37.010
Modern commentators,
especially Libertarians

00:11:37.010 --> 00:11:40.360
want a very narrowly drawn
account of public use

00:11:40.360 --> 00:11:43.460
and disagree with the
breadth of the doctrine

00:11:43.460 --> 00:11:45.580
as I described it to you.

00:11:45.580 --> 00:11:47.710
And so there's a lot of
activism around that.

00:11:47.710 --> 00:11:49.980
There's been some state
laws that's been enacted

00:11:49.980 --> 00:11:52.220
to try to raise the floor there.

00:11:52.220 --> 00:11:55.150
The Federal definition of
public use is just a floor

00:11:55.150 --> 00:11:56.660
and states can go beyond that

00:11:56.660 --> 00:11:58.910
and restrict the power of eminent domain

00:11:58.910 --> 00:12:00.410
more forcefully if they want to.

00:12:00.410 --> 00:12:01.810
And many have.

00:12:01.810 --> 00:12:03.720
- [Kim] So we've learned
that the takings clause

00:12:03.720 --> 00:12:04.710
of the Fifth Amendment

00:12:04.710 --> 00:12:07.160
prevents both Federal
and state governments

00:12:07.160 --> 00:12:09.900
from taking private
property for public use

00:12:09.900 --> 00:12:11.720
without just compensation.

00:12:11.720 --> 00:12:14.780
But there are a lot of
questions about what counts

00:12:14.780 --> 00:12:18.810
as private property, public
use or just compensation.

00:12:18.810 --> 00:12:21.240
In recent years debate
over the takings clause

00:12:21.240 --> 00:12:23.380
has centered on whether
government regulations

00:12:23.380 --> 00:12:26.040
about how a private
individual can use land

00:12:26.040 --> 00:12:28.500
also constitute a form of confiscation.

00:12:28.500 --> 00:12:31.630
And the extent of acceptable public uses

00:12:31.630 --> 00:12:33.870
for which the government
can seize property.

00:12:33.870 --> 00:12:35.650
To learn more about the Fifth Amendment,

00:12:35.650 --> 00:12:37.630
visit the National Constitution Centers

00:12:37.630 --> 00:12:40.530
interactive constitution
and Khan Academy's resources

00:12:40.530 --> 00:12:42.353
on U.S. government and politics.


Roe v. Wade

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:02.480
- [Kim] Hi, this is Kim from Khan Academy.

00:00:02.480 --> 00:00:05.420
Today we're learning more
about Roe versus Wade,

00:00:05.420 --> 00:00:08.000
the 1973 Supreme Court case

00:00:08.000 --> 00:00:10.720
that ruled that the
right of privacy extends

00:00:10.720 --> 00:00:13.240
to a woman's decision to have an abortion.

00:00:13.240 --> 00:00:15.130
To learn more about Roe versus Wade,

00:00:15.130 --> 00:00:17.350
I spoke to two experts on the case.

00:00:17.350 --> 00:00:19.840
Clarke Forsythe is senior counsel

00:00:19.840 --> 00:00:21.800
for Americans United for Life

00:00:21.800 --> 00:00:24.190
and the author of Abuse of Discretion:

00:00:24.190 --> 00:00:26.490
The Inside Story of Roe Versus Wade.

00:00:26.490 --> 00:00:29.950
Melissa Murray is the Alexander
F. And May T. Morrison

00:00:29.950 --> 00:00:32.550
Professor of law at Berkeley Law School

00:00:32.550 --> 00:00:35.050
where she also serves
as the faculty director

00:00:35.050 --> 00:00:37.780
for the Center on Reproductive
Rights and Justice.

00:00:37.780 --> 00:00:41.310
Mr. Forsythe, could you set
the stage for us a little bit?

00:00:41.310 --> 00:00:43.400
What was going on at this time period?

00:00:43.400 --> 00:00:46.140
- [Clarke] Well, there
were efforts in the 1960s

00:00:46.140 --> 00:00:49.920
to repeal abortion laws in the states,

00:00:49.920 --> 00:00:54.920
and when abortion
activists were dissatisfied

00:00:55.070 --> 00:00:58.170
with those efforts, they
decided to go into the courts.

00:00:58.170 --> 00:01:03.170
And around 1969, they took
some cases into the courts,

00:01:04.700 --> 00:01:08.310
and ultimately there were 20 or more cases

00:01:08.310 --> 00:01:11.510
challenging state laws in the courts

00:01:11.510 --> 00:01:15.560
between 1969 and 1973.

00:01:17.950 --> 00:01:22.330
And Roe versus Wade was a case from Texas.

00:01:22.330 --> 00:01:25.300
- [Melissa] Roe was
litigated in the early 1970s.

00:01:25.300 --> 00:01:28.400
It was a period of enormous
change in the United States.

00:01:28.400 --> 00:01:30.740
We were beginning to see the beginnings

00:01:30.740 --> 00:01:32.150
of the Women's Rights Movements,

00:01:32.150 --> 00:01:34.210
the beginnings of the Gay Rights Movement,

00:01:34.210 --> 00:01:37.500
and, of course, the Civil
Rights Movement of the 1960s

00:01:37.500 --> 00:01:40.410
was moving in a lot of
different directions.

00:01:40.410 --> 00:01:43.130
At the time, the question of abortion

00:01:43.130 --> 00:01:45.870
was very much on the minds of lots

00:01:45.870 --> 00:01:47.490
of different state legislatures

00:01:47.490 --> 00:01:50.780
because there had been moves to liberalize

00:01:50.780 --> 00:01:53.450
much of the criminal law
that dealt with matters

00:01:53.450 --> 00:01:57.250
of sex and sexuality, including abortion.

00:01:57.250 --> 00:02:01.040
At the time, four
states, New York, Alaska,

00:02:01.040 --> 00:02:04.760
Hawaii and I believe Washington
had actually taken steps

00:02:04.760 --> 00:02:08.610
to repeal their laws
criminalizing abortion,

00:02:08.610 --> 00:02:11.710
and about 13 other
states had taken efforts

00:02:11.710 --> 00:02:15.280
to liberalize their laws
criminalizing abortions,

00:02:15.280 --> 00:02:20.280
but in a number of other
states, at least 20 or more,

00:02:20.340 --> 00:02:22.350
there remained on the books laws

00:02:22.350 --> 00:02:24.640
that absolutely criminalized abortion

00:02:24.640 --> 00:02:28.070
except in situations where
it would be necessary

00:02:28.070 --> 00:02:30.890
to preserve the woman's health or life

00:02:30.890 --> 00:02:35.120
or in cases of rape,
incest or fetal anomaly.

00:02:35.120 --> 00:02:37.330
- [Clarke] Abortion rights attorneys

00:02:37.330 --> 00:02:41.907
sought plaintiffs who could
challenge the Texas law

00:02:41.907 --> 00:02:43.190
and the Georgia law.

00:02:43.190 --> 00:02:46.610
There were two attorneys from Texas

00:02:46.610 --> 00:02:51.610
who found Norma McCorvey who
gave the pseudonym of Jane Roe

00:02:54.110 --> 00:02:56.100
for purposes of protecting her privacy,

00:02:56.100 --> 00:02:59.790
and she became the nominal plaintiff.

00:02:59.790 --> 00:03:03.590
- [Melissa] And so Norma
McCorvey brought this case.

00:03:03.590 --> 00:03:07.720
She was a 22 year-old woman
living in Dallas County, Texas

00:03:07.720 --> 00:03:10.500
who found herself pregnant
for the third time.

00:03:10.500 --> 00:03:11.970
She was unmarried.

00:03:11.970 --> 00:03:14.870
Her first child has been born a daughter,

00:03:14.870 --> 00:03:17.510
and she'd ultimately signed over custody

00:03:17.510 --> 00:03:19.500
of her daughter to her mother to raise

00:03:19.500 --> 00:03:22.550
because she was having a
bit of an itinerant life,

00:03:22.550 --> 00:03:24.780
wasn't able to take care of her child.

00:03:24.780 --> 00:03:28.560
The second child that she
bore she gave up for adoption.

00:03:28.560 --> 00:03:31.320
And so when she found herself
pregnant for a third time,

00:03:31.320 --> 00:03:33.760
she wasn't willing to do
either of these things again

00:03:33.760 --> 00:03:37.080
and wanted to safely and
legally terminate her pregnancy,

00:03:37.080 --> 00:03:40.140
but this was impossible
under the Texas law.

00:03:40.140 --> 00:03:42.740
Texas had since the 19th century

00:03:42.740 --> 00:03:44.710
absolutely criminalized abortion

00:03:44.710 --> 00:03:46.750
except in cases where it was necessary

00:03:46.750 --> 00:03:48.770
for the health and safety of the mother.

00:03:48.770 --> 00:03:51.670
And so she then was
faced with the question

00:03:51.670 --> 00:03:53.210
of what was she going to do?

00:03:53.210 --> 00:03:55.140
And the only thing she
could think to do then

00:03:55.140 --> 00:03:57.170
was to actually challenge the law.

00:03:57.170 --> 00:04:00.550
So she was put in contact
with Sarah Weddington

00:04:00.550 --> 00:04:03.900
and Linda Coffee, two young
women who had recently graduated

00:04:03.900 --> 00:04:04.733
from law school.

00:04:04.733 --> 00:04:07.100
Sarah Weddington was only 26 years old

00:04:07.100 --> 00:04:10.630
at the time that she helped
Norma McCorvey bring this case.

00:04:10.630 --> 00:04:13.580
But they decided to sue the state of Texas

00:04:13.580 --> 00:04:16.120
to challenge the constitutionality

00:04:16.120 --> 00:04:18.330
of Texas's criminal abortion ban.

00:04:18.330 --> 00:04:21.750
- [Clarke] But as the history shows,

00:04:21.750 --> 00:04:25.030
there was no trial, there was no evidence,

00:04:25.030 --> 00:04:26.860
there were no expert witnesses.

00:04:26.860 --> 00:04:28.920
Jane Roe never testified.

00:04:28.920 --> 00:04:31.460
As you know, she never got an abortion.

00:04:31.460 --> 00:04:35.450
She gave birth and placed
her child for adoption.

00:04:35.450 --> 00:04:39.180
- [Kim] Okay, so Roe was Norma McCorvey.

00:04:39.180 --> 00:04:40.310
Who was Wade?

00:04:40.310 --> 00:04:43.540
- [Clarke] Henry Wade
was the district attorney

00:04:43.540 --> 00:04:48.540
for Dallas, Texas where the case was filed

00:04:48.550 --> 00:04:50.900
in federal district court.

00:04:50.900 --> 00:04:55.230
- [Kim] So this case, I
assume kind of winds it way

00:04:55.230 --> 00:04:57.310
through the courts,

00:04:57.310 --> 00:04:59.910
and how did the Supreme Court rule?

00:04:59.910 --> 00:05:04.140
- [Clarke] The justices declared the Texas

00:05:04.140 --> 00:05:07.870
and Georgia laws unconstitutional

00:05:07.870 --> 00:05:12.310
and then rewrote a national law,

00:05:12.310 --> 00:05:16.300
a national abortion law in which they said

00:05:16.300 --> 00:05:19.640
that the states could not
regulate or limit abortion

00:05:19.640 --> 00:05:21.270
in the first trimester.

00:05:21.270 --> 00:05:24.870
They could regulate more
in the second trimester,

00:05:24.870 --> 00:05:27.410
the second three months of pregnancy

00:05:27.410 --> 00:05:29.750
to protect maternal health,

00:05:29.750 --> 00:05:32.280
and they could regulate
in the last three months

00:05:32.280 --> 00:05:35.060
of pregnancy, the last trimester

00:05:35.060 --> 00:05:37.810
to protect maternal health or fetal life.

00:05:37.810 --> 00:05:40.230
The attorneys for the plaintiffs claimed

00:05:40.230 --> 00:05:44.200
that abortion fell within
the right to privacy

00:05:44.200 --> 00:05:47.700
even though privacy is not in
the text of the Constitution.

00:05:47.700 --> 00:05:49.840
They said it was derived or based

00:05:49.840 --> 00:05:53.700
in the language of the 14th
Amendment of the Constitution

00:05:53.700 --> 00:05:55.810
even though the 14th
Amendment doesn't say anything

00:05:55.810 --> 00:05:58.150
about abortion or the unborn child.

00:05:58.150 --> 00:06:00.800
It just uses the term liberty.

00:06:00.800 --> 00:06:04.585
And ultimately the Court said
that the right to abortion

00:06:04.585 --> 00:06:06.300
was part of the right to privacy

00:06:06.300 --> 00:06:07.970
based on the 14th Amendment.

00:06:07.970 --> 00:06:08.820
- [Kim] That's very interesting.

00:06:08.820 --> 00:06:11.040
So I've learned through
many of these interviews

00:06:11.040 --> 00:06:12.950
that this right to privacy is something

00:06:12.950 --> 00:06:15.440
that is never actually explicitly stated

00:06:15.440 --> 00:06:17.490
throughout the Bill of Rights,

00:06:17.490 --> 00:06:20.980
but there's a penumbra of privacy

00:06:20.980 --> 00:06:22.700
that you see in a few ways.

00:06:22.700 --> 00:06:24.130
What was the court's reasoning

00:06:24.130 --> 00:06:25.370
that it was abortion

00:06:25.370 --> 00:06:28.660
that could fall under
this zone of privacy?

00:06:28.660 --> 00:06:30.830
- [Clarke] If you read the Roe opinion,

00:06:30.830 --> 00:06:33.403
on page 152 of the Roe opinion,

00:06:34.730 --> 00:06:37.099
Justice Blackmon starts
out by saying that,

00:06:37.099 --> 00:06:41.730
he sites a string of
cases since about 1910,

00:06:41.730 --> 00:06:44.409
a string of Supreme Court cases

00:06:44.409 --> 00:06:46.700
and says that these lead
to the right of privacy,

00:06:46.700 --> 00:06:50.120
and we think abortion or
that the right of privacy

00:06:50.120 --> 00:06:52.740
is broad enough to encompass abortion.

00:06:52.740 --> 00:06:56.490
But then four pages later on page 156,

00:06:56.490 --> 00:06:58.360
Blackmon turns around and says,

00:06:58.360 --> 00:07:02.140
but abortion, because it
involves the taking of a life,

00:07:02.140 --> 00:07:06.590
is inherently different
from all those other cases

00:07:06.590 --> 00:07:08.510
that make up the right of privacy.

00:07:08.510 --> 00:07:11.210
- [Melissa] So the right of
privacy doesn't actually come

00:07:11.210 --> 00:07:12.580
from Roe versus Wade.

00:07:12.580 --> 00:07:16.400
It comes from a case decided
about eight years earlier

00:07:16.400 --> 00:07:19.910
in 1965 called Griswold
versus Connecticut.

00:07:19.910 --> 00:07:23.610
In Griswold, at issue was
a Connecticut state statute

00:07:23.610 --> 00:07:26.310
that made it a crime to use contraception

00:07:26.310 --> 00:07:30.270
or even to counsel patients
about contraceptions.

00:07:30.270 --> 00:07:32.900
Planned Parenthood League of Connecticut

00:07:32.900 --> 00:07:36.720
opened up a birth control clinic
in New Haven, Connecticut.

00:07:36.720 --> 00:07:39.650
They were promptly arrested,
and the clinic was closed,

00:07:39.650 --> 00:07:41.920
and then they were able
to bring this case.

00:07:41.920 --> 00:07:44.990
And they argued that the right to be able

00:07:44.990 --> 00:07:47.650
to use contraception was
the right of the individual,

00:07:47.650 --> 00:07:49.500
the right of the doctor to advise patients

00:07:49.500 --> 00:07:52.220
about contraception was
also an individual right.

00:07:52.220 --> 00:07:54.180
And the Court in an opinion authored

00:07:54.180 --> 00:07:57.320
by William O. Douglas agrees with them,

00:07:57.320 --> 00:08:00.750
and the Court articulates
for the first time

00:08:00.750 --> 00:08:02.390
this right of privacy,

00:08:02.390 --> 00:08:06.690
and this is a right that the
majority in Griswold says

00:08:06.690 --> 00:08:09.230
has actually been percolating
in the Court's decisions

00:08:09.230 --> 00:08:10.103
for a some time.

00:08:10.103 --> 00:08:13.620
- [Kim] Did any of the justices
dissent in the Roe decision,

00:08:13.620 --> 00:08:15.430
and if so, why?

00:08:15.430 --> 00:08:17.950
- [Clarke] Well, there were two dissents

00:08:17.950 --> 00:08:22.460
by Justice White and by Justice Rehnquist,

00:08:22.460 --> 00:08:24.820
and Justice White said that

00:08:25.900 --> 00:08:30.900
the Court was engaging
in raw judicial power

00:08:31.140 --> 00:08:36.140
and that the justices
did not have the right

00:08:38.132 --> 00:08:41.830
or the authority to strike
down the abortion laws

00:08:41.830 --> 00:08:45.740
of the states and could not rely upon

00:08:45.740 --> 00:08:48.440
a doctrine called substantive due process.

00:08:48.440 --> 00:08:52.523
Justice Rehnquist said
that there us clear,

00:08:53.690 --> 00:08:58.520
historical evidence that many
states passed abortion limits

00:08:58.520 --> 00:09:01.030
and prohibitions precisely at the time

00:09:01.030 --> 00:09:05.080
of the framing of the 14th
Amendment in the 1860s

00:09:05.080 --> 00:09:09.670
leading up to 1868 and that
the evidentiary history,

00:09:09.670 --> 00:09:12.850
this history of state limits
and prohibitions on abortion

00:09:12.850 --> 00:09:15.700
contradicted any proposition
that the 14th Amendment

00:09:15.700 --> 00:09:18.360
was intended to include
a right to abortion,

00:09:18.360 --> 00:09:21.860
and that was kind of the
heart of his dissent.

00:09:21.860 --> 00:09:25.080
- [Kim] So Roe was not the last word

00:09:25.080 --> 00:09:27.030
on abortion in the United States.

00:09:27.030 --> 00:09:28.570
There have been several later cases

00:09:28.570 --> 00:09:29.980
that were important to this, as well,

00:09:29.980 --> 00:09:31.970
like Planned Parenthood versus Casey

00:09:31.970 --> 00:09:34.350
or Whole Woman's Health
versus Hellerstedt.

00:09:34.350 --> 00:09:36.530
Can you talk a little
bit about how those cases

00:09:36.530 --> 00:09:38.940
have altered the scope
of the right to abortion?

00:09:38.940 --> 00:09:42.550
- [Melissa] As soon as
Roe is decided in 1973,

00:09:42.550 --> 00:09:45.240
there is an effort to sort of roll it back

00:09:45.240 --> 00:09:47.120
and hem it in a little bit.

00:09:47.120 --> 00:09:49.580
Frank Church, who's a senator from Idaho,

00:09:49.580 --> 00:09:51.780
announces the Church Amendment,

00:09:51.780 --> 00:09:54.020
which basically says that physicians

00:09:54.020 --> 00:09:56.820
don't have to perform abortions

00:09:56.820 --> 00:09:59.730
if doing so would conflict
with their conscience

00:09:59.730 --> 00:10:01.090
or conscience beliefs.

00:10:01.090 --> 00:10:03.090
So again, that's one opportunity

00:10:03.090 --> 00:10:05.220
to sort of limit the reach of this right

00:10:05.220 --> 00:10:06.930
by limiting the number of providers

00:10:06.930 --> 00:10:09.840
who are available to offer abortions.

00:10:09.840 --> 00:10:13.520
- [Clarke] In fact, the
Court has kind of cut back

00:10:13.520 --> 00:10:18.160
on Roe versus Wade in
four cases over the years.

00:10:18.160 --> 00:10:21.130
Harris versus McCrae,
involving abortion funding,

00:10:21.130 --> 00:10:25.010
Planned Parenthood versus
Casey, and in other cases,

00:10:25.010 --> 00:10:26.840
they've given more
deference to the states,

00:10:26.840 --> 00:10:30.730
allowed the states to
pass more and more limits

00:10:30.730 --> 00:10:33.020
at least around the margins

00:10:33.020 --> 00:10:35.757
even though they've continued holding

00:10:36.842 --> 00:10:39.460
to the basic right that Roe created

00:10:39.460 --> 00:10:40.870
that there is a right to abortion

00:10:40.870 --> 00:10:44.420
for virtually any reason
at any time of pregnancy.

00:10:44.420 --> 00:10:46.940
That's still the scope of the right,

00:10:46.940 --> 00:10:48.980
but they've allowed marginal regulations

00:10:48.980 --> 00:10:50.810
like limits on public funding,

00:10:50.810 --> 00:10:53.940
parental notice and consent,
informed consent laws.

00:10:53.940 --> 00:10:58.940
But then the Court flip flopped
in 2016, in June if 2016

00:10:59.260 --> 00:11:01.690
in Whole Woman's Health
versus Hellerstedt.

00:11:01.690 --> 00:11:03.320
- [Melissa] The case makes its way

00:11:03.320 --> 00:11:06.373
to the Supreme Court, and in an opinion

00:11:06.373 --> 00:11:09.190
that authored by Justice Stephen Breyer,

00:11:09.190 --> 00:11:10.890
and it's only an eight person court

00:11:10.890 --> 00:11:14.730
because Justice Scalia passes
away in February of 2016,

00:11:14.730 --> 00:11:16.790
so just eight people on the Court.

00:11:16.790 --> 00:11:19.130
In this decision that's
a five to three decision,

00:11:19.130 --> 00:11:21.460
Justice Stephen Breyer notes

00:11:21.460 --> 00:11:24.230
that the provisions that were challenged

00:11:24.230 --> 00:11:28.010
do not offer the medical
benefits that they claim to offer

00:11:28.010 --> 00:11:31.280
sufficient to justify
the burdens on access

00:11:31.280 --> 00:11:33.460
that each of those provisions imposes.

00:11:33.460 --> 00:11:36.260
- [Kim] What do you see as
the future of Roe versus Wade?

00:11:36.260 --> 00:11:38.487
- [Clarke] Well, the Court has failed

00:11:38.487 --> 00:11:39.500
as a national abortion control board.

00:11:39.500 --> 00:11:42.530
It cannot monitor abortion.

00:11:42.530 --> 00:11:44.330
It can't intervene.

00:11:44.330 --> 00:11:47.360
It can't regulate or legislate itself.

00:11:47.360 --> 00:11:50.130
It can't act as public
health administrators.

00:11:50.130 --> 00:11:51.960
It can't investigate.

00:11:51.960 --> 00:11:56.530
And I believe it's absolutely certain

00:11:56.530 --> 00:11:57.920
that the Court, sooner or later,

00:11:57.920 --> 00:12:01.410
will have to overturn the
Roe versus Wade decision

00:12:01.410 --> 00:12:04.370
because of this failure and
return the issue to the states.

00:12:04.370 --> 00:12:06.630
- [Melissa] When we are
talking about repealing

00:12:06.630 --> 00:12:10.330
or reforming these laws
in the 1960s and 1970s,

00:12:10.330 --> 00:12:12.640
it's also around a social movement

00:12:12.640 --> 00:12:14.590
where one of the critical questions

00:12:14.590 --> 00:12:17.600
is what will be the role
of women going forth

00:12:17.600 --> 00:12:19.490
in a modern society?

00:12:19.490 --> 00:12:22.610
When the questions of contraception
come before the Court,

00:12:22.610 --> 00:12:24.560
one of the questions is
whether women will be allowed

00:12:24.560 --> 00:12:27.170
to choose when and how to have children,

00:12:27.170 --> 00:12:29.890
whether they can space
the timing of births

00:12:29.890 --> 00:12:31.530
to accommodate careers.

00:12:31.530 --> 00:12:34.030
It's the same issue that
comes up in abortion.

00:12:34.030 --> 00:12:36.610
Like this is allowing women freedom

00:12:36.610 --> 00:12:38.470
to be able to go into the workforce,

00:12:38.470 --> 00:12:40.750
to determine when and how
they will become mothers,

00:12:40.750 --> 00:12:44.670
and so it's not surprising
that the same questions

00:12:44.670 --> 00:12:47.420
that arose in the 19th century
about the place of women,

00:12:47.420 --> 00:12:49.230
about what happens in a society

00:12:49.230 --> 00:12:51.890
that's undergoing change,
whether it's immigration

00:12:51.890 --> 00:12:54.520
or changes in the
demography of the country,

00:12:54.520 --> 00:12:57.620
are also coming up in the 1960s and 1970s

00:12:57.620 --> 00:12:59.640
at a time of incredible social change,

00:12:59.640 --> 00:13:03.020
and I think abortion and
these rights involving

00:13:03.020 --> 00:13:05.250
a woman's role really do come to the fore

00:13:05.250 --> 00:13:07.000
and are incredibly controversial.

00:13:07.000 --> 00:13:08.940
- [Kim] So we've learned that the decision

00:13:08.940 --> 00:13:11.820
to legalize abortion in Roe versus Wade

00:13:11.820 --> 00:13:13.870
was based on the right of privacy,

00:13:13.870 --> 00:13:17.160
which the Court has inferred
from the due process clause

00:13:17.160 --> 00:13:18.520
of the 14th Amendment.

00:13:18.520 --> 00:13:21.310
Since the Roe decision,
a number of other cases

00:13:21.310 --> 00:13:24.200
have set limits on abortion
and abortion clinics.

00:13:24.200 --> 00:13:26.710
Clarke Forsythe argues
that the Supreme Court

00:13:26.710 --> 00:13:28.710
has failed in regulating abortion

00:13:28.710 --> 00:13:31.090
and that the issue should
be returned to the states.

00:13:31.090 --> 00:13:33.030
Melissa Murray, by contrast,

00:13:33.030 --> 00:13:35.990
suggests that the
decision in Roe is crucial

00:13:35.990 --> 00:13:38.440
to giving women the freedom
to join the workforce

00:13:38.440 --> 00:13:40.660
and make decisions about
when to have children.

00:13:40.660 --> 00:13:42.360
To learn more about this case,

00:13:42.360 --> 00:13:44.400
visit the National Constitution Center's

00:13:44.400 --> 00:13:47.520
Interactive Constitution
and Khan Academy's resources

00:13:47.520 --> 00:13:49.453
on US government and politics.