t a(j) = 2*j**4 + 3*j**3 - 10*j**2 + j - 4. Let o(l) = l**4 + l**2 - l + 1. Let x(k) = a(k) + 4*o(k). Factor x(q).
3*q*(q - 1)*(q + 1)*(2*q + 1)
Let y(d) = 24*d**3 + 9*d**2 - 57*d + 57. Let o(s) = 10 - 4*s**2 - 7*s + 3*s**3 - 3 + 5*s**2. Let k(j) = 33*o(j) - 4*y(j). Factor k(u).
3*(u - 1)**2*(u + 1)
Let n(k) be the third derivative of k**2 + 0*k + 1/30*k**5 + 0 - 1/3*k**3 - 1/12*k**4 + 1/60*k**6. Suppose n(z) = 0. What is z?
-1, 1
Let l(h) be the first derivative of h**3/7 - h**2/7 + 2. Factor l(n).
n*(3*n - 2)/7
Let d = 12 - 10. Let 15*u**d + 0*u - 1 + 0 - 5 - 9*u = 0. Calculate u.
-2/5, 1
Let x(f) be the third derivative of -7/3*f**4 - 19/10*f**5 + 0 - 4/3*f**3 + 3*f**2 - 3/5*f**6 + 0*f. Factor x(k).
-2*(3*k + 2)**2*(4*k + 1)
Let y(g) = 3*g**2 - 1. Let l(m) = -m**2. Let c(w) = -2*l(w) - y(w). Factor c(z).
-(z - 1)*(z + 1)
Determine n, given that 1/6*n**2 + 1/3*n + 1/6 = 0.
-1
Let y(c) be the third derivative of c**7/840 + c**6/160 + c**5/240 - c**4/32 - c**3/12 + 2*c**2. Factor y(d).
(d - 1)*(d + 1)**2*(d + 2)/4
Suppose -5*c**2 + 6 - 5*c + 5*c + 24 - 5*c = 0. Calculate c.
-3, 2
Let q(j) = 7*j**4 + 11*j**3 + 5*j**2 + j. Let h be (-10)/(-5)*1*-12. Let m(x) = -x**4 - x**3 - x**2. Let w(a) = h*m(a) - 3*q(a). Factor w(k).
3*k*(k - 1)**3
Suppose -4*a = -42 - 38. Let k = a + -58/3. Factor -k + 4/3*d + 2*d**2.
2*(d + 1)*(3*d - 1)/3
Let l be (6/(-8))/((-68)/(-192)). Let m = 28/51 - l. Find x such that -14*x**4 + m*x + 0 - 8/3*x**2 - 58/3*x**3 = 0.
-1, -2/3, 0, 2/7
Let x(q) be the first derivative of 3*q**3 + 2*q - 5/4*q**4 + 1/5*q**5 - 7/2*q**2 + 1. Factor x(v).
(v - 2)*(v - 1)**3
Let l(w) = -7*w**3 - 15*w**2 - 12*w - 4. Let d(q) = -15*q**3 - 31*q**2 - 24*q - 8. Let b(k) = -3*d(k) + 7*l(k). Factor b(x).
-4*(x + 1)**3
Let o(a) = -a**2 + 7*a - 1. Let i be o(6). Let j(r) be the third derivative of -1/15*r**3 - 2*r**2 + 0*r + 1/150*r**i + 0 + 0*r**4. Factor j(x).
2*(x - 1)*(x + 1)/5
Let k(d) be the second derivative of 0 - 1/6*d**4 + 1/3*d**3 + d - 1/10*d**5 + d**2. Factor k(g).
-2*(g - 1)*(g + 1)**2
Suppose 6*z - z = 5*w + 15, 5*z + w + 3 = 0. Let l be -1 + -4*5/(-20). Determine p so that -2/7*p**3 + z*p**2 + 2/7*p + l = 0.
-1, 0, 1
Factor 1/3*a - 1/3*a**2 + 0.
-a*(a - 1)/3
Let w(g) = g**3 - 6*g**2 + 4*g + 7. Let k be w(5). Let f = -199 - -201. Suppose -k*t**3 - 4/3*t**4 + f*t + 2/3*t**2 + 2/3 = 0. Calculate t.
-1, -1/2, 1
Let j(y) be the first derivative of y**7/3360 - y**6/480 + y**5/240 + 7*y**3/3 + 2. Let n(m) be the third derivative of j(m). Factor n(w).
w*(w - 2)*(w - 1)/4
Let l(h) be the first derivative of -h**3/27 + 17*h**2/9 - 289*h/9 - 6. Suppose l(x) = 0. What is x?
17
Let b = 180 + -180. Factor -4/5*t**2 + 2*t**3 - 8/5*t**4 + 0*t + 2/5*t**5 + b.
2*t**2*(t - 2)*(t - 1)**2/5
Let f be (-41)/(-3) - 3/(-6)*6. What is w in -4*w**2 + 56/3*w + 16/3 - 110/3*w**3 + f*w**4 = 0?
-2/5, 1, 2
Let j(o) = -4*o - 21. Let d be j(-6). Let k(m) be the first derivative of 0*m - 1/6*m**4 + 2 + 2/9*m**d + 0*m**2. What is q in k(q) = 0?
0, 1
Let v = -650 + 652. Suppose -2*c**4 - 4/5*c - 18/5*c**3 - 14/5*c**v - 2/5*c**5 + 0 = 0. Calculate c.
-2, -1, 0
Let f = 0 + 5. Factor -2*g + f*g - g**2 - 4 + g.
-(g - 2)**2
Let w = -167/2 - -84. Factor 1/2 + w*b**2 - b.
(b - 1)**2/2
Let p = 0 + 4. Suppose p*l + 8 = 6*l. Factor -2*r**2 + 5*r**l + r**4 - 4*r**4.
2*r**2*(r - 1)*(r + 1)
Let k = 5789/2172 + 1/724. Factor -k*y**2 + 8*y - 6.
-2*(2*y - 3)**2/3
Let c(q) be the third derivative of 1/24*q**4 + 1/336*q**8 - 1/30*q**5 + 0 + 1/6*q**3 + 1/210*q**7 - 1/60*q**6 + 0*q - q**2. Factor c(z).
(z - 1)**2*(z + 1)**3
Let g be 6/9 + (-10)/15. Determine b, given that 2/7*b**3 - 2/7*b**2 + 0*b + g = 0.
0, 1
Let w = -249/5 + 50. Solve 0 - 2/5*l + w*l**2 = 0 for l.
0, 2
Let p(s) = -s**3. Let w(n) = -5*n**3 - 6*n**2 - 6*n - 2. Let k(g) = -6*p(g) + 2*w(g). Find a such that k(a) = 0.
-1
Let c(j) be the third derivative of -5*j**8/48 + 5*j**7/7 - 29*j**6/24 - 11*j**5/6 + 15*j**4/2 - 20*j**3/3 + 14*j**2 - 2*j. Determine v so that c(v) = 0.
-1, 2/7, 1, 2
Let w(v) be the second derivative of -2/7*v**7 + 3*v + 9/10*v**5 - 7/6*v**4 + 2*v**2 - v**3 + 0 + 1/3*v**6. Suppose w(s) = 0. Calculate s.
-1, -2/3, 1/2, 1
Let t(l) be the second derivative of -l**8/30240 - l**7/2835 - l**6/648 - l**5/270 + l**4/12 - 3*l. Let i(c) be the third derivative of t(c). Factor i(d).
-2*(d + 1)**2*(d + 2)/9
Let k(s) = -2*s**2 + s + 3. Let u be k(0). Solve 0*h**u - 2*h**3 + 3*h**5 + 8*h - 4*h**3 - 5*h = 0.
-1, 0, 1
Let u be (-39)/(-60) - (-6)/(-15). Let w(j) be the first derivative of u*j**4 + 1/2*j - 2 - 1/3*j**3 + 1/10*j**5 - 1/4*j**2 - 1/12*j**6. Factor w(q).
-(q - 1)**3*(q + 1)**2/2
Let v(h) be the third derivative of 0*h + 1/80*h**5 + 0 + 3/32*h**4 + h**2 + 1/4*h**3. Let v(s) = 0. What is s?
-2, -1
Let c(p) be the first derivative of 0*p**2 - 1/3*p**3 - 10 + 4*p. Factor c(o).
-(o - 2)*(o + 2)
Let r(k) be the first derivative of 0*k**3 + 1/2*k**4 + 0*k + 4 - k**2. Factor r(s).
2*s*(s - 1)*(s + 1)
Let p = -21599/54 - -400. Let d(o) be the second derivative of -5*o - 4/9*o**2 + 4/27*o**3 + 0 - p*o**4. Factor d(r).
-2*(r - 2)**2/9
Factor -275/4*x**3 - 15*x + 125/4*x**4 - 70*x**2 + 0.
5*x*(x - 3)*(5*x + 2)**2/4
Solve 1/5*v**2 + 0 + 1/5*v = 0 for v.
-1, 0
Let k(x) be the second derivative of -x**5/80 + x**4/24 - x**3/24 + 8*x. Let k(b) = 0. Calculate b.
0, 1
Let n(p) be the first derivative of -p**7/140 + p**5/40 - 7*p**2/2 + 7. Let b(l) be the second derivative of n(l). Factor b(c).
-3*c**2*(c - 1)*(c + 1)/2
Suppose -4*k - 14 = 2*f + 20, 4*f - 2*k + 18 = 0. Let o = f + 8. Factor -1/2*d - o + 1/2*d**3 + d**2.
(d - 1)*(d + 1)*(d + 2)/2
Let d(n) be the third derivative of -11/3*n**4 + n**2 - 3*n**5 + 0*n - 27/20*n**6 - 9/35*n**7 + 0 - 8/3*n**3. Solve d(h) = 0 for h.
-1, -2/3
Let d(l) be the first derivative of 2 + 0*l**2 - 1/42*l**4 + 2*l + 1/21*l**3. Let o(y) be the first derivative of d(y). Factor o(z).
-2*z*(z - 1)/7
Let s = 1 - -3. Find g such that g**2 - 3*g**s - 7*g**2 - 13*g**3 + 22*g**3 = 0.
0, 1, 2
Determine u, given that 18/7*u**2 - 6/7*u**3 + 0 - 2/7*u**5 - 10/7*u**4 + 0*u = 0.
-3, 0, 1
Let t(x) be the second derivative of -x**6/6 - x**5 + 8*x + 1. Determine c, given that t(c) = 0.
-4, 0
Suppose w + 2*v = 3*v + 6, 5*w + 3*v = -2. Let k = -5 - -8. Factor 4 + 0*y**w - k*y**2 - 4*y + 4*y**2.
(y - 2)**2
Let k(j) be the first derivative of -2*j**3 + 1 + 6*j + j**3 + 0*j**3 + 0*j. Let c(h) = -h - 1. Let v(x) = 6*c(x) + k(x). Factor v(w).
-3*w*(w + 2)
Suppose -22 = 4*y + 42. Let k be y/(-12) + (-2)/3. Factor -k*x**3 + 4/3*x**2 - 2/3*x + 0.
-2*x*(x - 1)**2/3
Let q(o) = -o**2 - o. Let z(b) = 9*b**2 - 12*b - 21. Let d(u) = -6*q(u) - z(u). Factor d(n).
-3*(n - 7)*(n + 1)
Let o be (465/27)/5 + -3. Determine d so that -2/9*d + 0 - 2/9*d**3 - o*d**2 = 0.
-1, 0
Suppose 8 = i + 3*i. Suppose 3*d - 17 = -4*j, 4*j - 20 = -i*d - 2*d. Factor -n + 5*n + j*n**2 - 5*n**2 + 2*n.
-3*n*(n - 2)
Factor -6/5*h**5 + 0 + 8/5*h**3 + 22/5*h**4 + 0*h + 0*h**2.
-2*h**3*(h - 4)*(3*h + 1)/5
Suppose -4/5 + 24/5*y - 9/5*y**2 - 11/5*y**3 = 0. What is y?
-2, 2/11, 1
Let p(w) be the third derivative of w**8/50400 - w**7/4200 + w**6/900 + w**5/60 - 3*w**2. Let t(b) be the third derivative of p(b). Find u such that t(u) = 0.
1, 2
Let w(x) be the first derivative of x**4/18 - 2*x**3/9 + 4*x + 4. Let a(l) be the first derivative of w(l). Factor a(f).
2*f*(f - 2)/3
Let o(b) = -4*b**2 - 4*b. Let t(x) = x**2. Let h(k) = 7*k**2 + k. Let c be h(-1). Let m(a) = c*t(a) + o(a). Factor m(v).
2*v*(v - 2)
Let z(y) = y**3 + 4*y**2 - 6*y - 5. Let u be z(-5). Factor -6*k**2 + 6*k**4 + 3*k - 9*k**5 + 6*k**5 + u*k.
-3*k*(k - 1)**3*(k + 1)
Let x(f) be the first derivative of 4/15*f**3 + 1/30*f**6 + 1/10*f**2 - 1/10*f**4 - 4 - 2/25*f**5 - 2/5*f. Determine a, given that x(a) = 0.
-1, 1, 2
Let q(h) be the first derivative of h**4/14 + 10*h**3/21 + h**2 + 6*h/7 + 28. Find l, given that q(l) = 0.
-3, -1
Suppose -9 = 226*s - 229*s. Let j(o) be the first derivative of 3/16*o**4 + 0*o + 1/8*o**2 - 1/4*o**s - 1/20*o**5 + 3. Factor j(d).
-d*(d - 1)**3/4
Let n(g) = -g**3 - 5*g**2 - 2*g + 5. Let h be n(-4). Let f be (-2)/h + 21/9. Factor -3*l**f - l**3 + 3*l**3 - 2*l**4 - l**3.
-2*l**3*(l + 1)
Let j(i) be the first derivative of i**9/16632 - i**8/9240 - i**7/4620 + i**6/1980 - 5*i**3/