for r.
-1, 1
Let q(h) be the second derivative of -h**7/28 + h**6/20 + 3*h**5/40 - h**4/8 - 12*h. Factor q(n).
-3*n**2*(n - 1)**2*(n + 1)/2
Let p(j) = j - 5. Let f be p(5). Suppose 2*l + 6 - 22 = -4*a, 0 = -2*l + 4. Solve 0*i**2 + 0 - 1/4*i**a + 1/2*i**4 - 1/4*i**5 + f*i = 0 for i.
0, 1
Let d(x) be the third derivative of 2*x**7/105 - x**6/15 + x**5/15 + 4*x**2. Factor d(r).
4*r**2*(r - 1)**2
Let d be ((-100)/(-180))/(5/6). Solve -2/3*p**2 - 2/3*p + 2/3*p**3 + d = 0.
-1, 1
Find m, given that 1/2*m**2 - m + 1/2 = 0.
1
Let l(d) be the first derivative of -d**5/100 + d**4/60 + d**3/30 - d**2/10 - 2*d - 2. Let w(p) be the first derivative of l(p). Suppose w(h) = 0. What is h?
-1, 1
Let c be 1512/1540 - -1*(-4)/22. Factor -c*n**2 - 12/5 + 16/5*n.
-4*(n - 3)*(n - 1)/5
Let z(u) = 41*u**3 - 13*u**4 + 6 + 12*u**4 - 2*u - 3*u - 41*u**2. Let x(y) = y**4 - 27*y**3 + 27*y**2 + 3*y - 4. Let a(g) = -8*x(g) - 5*z(g). Factor a(r).
-(r - 2)*(r - 1)**2*(3*r + 1)
Let a = -106/9 + 5503/468. Let d = 3/13 - a. Let -1/2 + d*i + 1/4*i**2 = 0. What is i?
-2, 1
What is z in -6 + 100*z**2 + 10 + 28*z**4 + 4*z**5 + 76*z**3 + 64*z + 0*z**5 + 12 = 0?
-2, -1
What is k in -8*k**2 + 8*k**2 - k**2 + 4*k - 4 = 0?
2
Let r = 19 + -19. Factor 3/2*m + 3/2*m**2 + r.
3*m*(m + 1)/2
Suppose -5*z = -1 - 4. Find s such that 4*s**2 + z - 3*s**2 + 0*s**2 - 2*s = 0.
1
Suppose -23/4*a**2 + 119/4*a**4 - 67/4*a**3 + 4*a - 49/4*a**5 + 1 = 0. Calculate a.
-2/7, 1
Let q be 13/(-13) + 11/9. Let h be 30/189 - (-10)/35. Suppose 0 + h*g - q*g**2 = 0. What is g?
0, 2
Factor 2*h**3 - 12*h**3 + 2*h**4 + 2*h**3 + 10*h**2 - 4*h.
2*h*(h - 2)*(h - 1)**2
Let z(t) = -4*t - 4*t**2 + 1 + 5*t + 3*t**2. Let m be 1 - (-1)/(2/(-6)). Let j(n) = -3*n - 1. Let r(q) = m*z(q) - 2*j(q). Let r(w) = 0. What is w?
-2, 0
Let b(g) be the first derivative of -1/2*g**2 + 1/4*g**4 - 3 - g + 1/3*g**3. Suppose b(u) = 0. What is u?
-1, 1
Suppose 5*a - 21 = -4*y + 5, 0 = 4*a - 2*y. Let d(t) be the first derivative of 1/7*t**a - 4/7*t + 4/21*t**3 - 1 - 1/14*t**4. Factor d(q).
-2*(q - 2)*(q - 1)*(q + 1)/7
Let f(x) = 5*x - 6. Let d be f(6). Solve d*g**3 + 0*g - 21*g**2 + 11*g**5 - 9*g + 18*g**4 + 3 - 35*g**5 + 9*g**3 = 0.
-1, -1/2, 1/4, 1
Factor 4 - 20/3*w + w**2.
(w - 6)*(3*w - 2)/3
Suppose 2*d + 3 = 9. Let -39/4*l**2 - 9*l - 9/2*l**d - 3 - 3/4*l**4 = 0. What is l?
-2, -1
Suppose -r - 5*d - 165 = 3*r, 0 = -3*r + 4*d - 116. Let y be (156/325)/((-3)/r). Let 42/5*x**2 + y*x + 18/5*x**3 + 8/5 = 0. What is x?
-1, -2/3
Let r = 2/79 - -152/237. Let h = r - 0. What is a in -2/3*a**3 + 0*a**2 + h*a - 1/3*a**4 + 1/3 = 0?
-1, 1
Let y(p) be the second derivative of p**7/21 + 2*p**6/15 - p**5/10 - p**4/3 - 10*p. Let y(f) = 0. Calculate f.
-2, -1, 0, 1
Factor -14*d + 16 - d**3 + 8*d**2 - 4*d - 2*d.
-(d - 4)*(d - 2)**2
Suppose 3*u + 140 = u. Let i be u/(-63)*21/5. Determine t so that 2/3 + 4*t**3 + 0*t - i*t**2 = 0.
-1/3, 1/2, 1
Let l(j) be the second derivative of -2*j**7/105 + j**6/30 + 2*j**5/15 + 5*j**2/2 - 5*j. Let m(g) be the first derivative of l(g). Find o such that m(o) = 0.
-1, 0, 2
Let x be 26/7 + (-2)/(-7). Factor -x*w**2 + w**3 + 2*w**2 - 2*w**3.
-w**2*(w + 2)
Let l(k) be the first derivative of 1/4*k**4 - 1/10*k**5 - 1/2*k - 1/12*k**6 + 1/3*k**3 + 3 - 1/4*k**2. Factor l(o).
-(o - 1)**2*(o + 1)**3/2
Let t(u) be the second derivative of -1/2*u**2 - 1/180*u**6 + 0 + 0*u**3 - 1/60*u**5 - 1/72*u**4 + 3*u. Let k(m) be the first derivative of t(m). Factor k(p).
-p*(p + 1)*(2*p + 1)/3
Let v(z) be the second derivative of -3*z**5/40 + z**4/4 - 7*z. Find m, given that v(m) = 0.
0, 2
Let n be 2/45*(714 - 2). Let z = n - 256/9. Find k, given that -1/5*k**5 - 16/5 - 16/5*k**3 + z*k + 7/5*k**4 + 8/5*k**2 = 0.
-1, 2
Let b be 33/36 - (-144)/(-192). Factor b + 1/6*o**2 + 1/3*o.
(o + 1)**2/6
Let z(g) = -42*g**2 - 21*g + 15. Let o(m) = -6*m**2 - 3*m + 2. Let i(y) = -15*o(y) + 2*z(y). Suppose i(u) = 0. What is u?
-1/2, 0
Let -2*z**4 + 7*z**5 - 9*z**5 - 2*z**3 + 3*z**4 - 5*z**4 = 0. Calculate z.
-1, 0
Let o(j) be the first derivative of j**2/2 - 8*j + 2. Let c be o(8). Let 2/7*a**2 + c - 2/7*a = 0. What is a?
0, 1
Let i(h) be the third derivative of -h**7/1260 + h**6/90 - 11*h**5/180 + h**4/6 - h**3/4 - 9*h**2. Factor i(u).
-(u - 3)**2*(u - 1)**2/6
Let w(t) be the third derivative of t**6/120 + t**5/20 + t**4/12 + 2*t**2. Factor w(x).
x*(x + 1)*(x + 2)
Let u(g) be the third derivative of g**2 - 1/540*g**6 + 0 - 4/27*g**3 - 2/27*g**4 - 1/54*g**5 + 0*g. Let u(l) = 0. Calculate l.
-2, -1
Let n(u) be the first derivative of u**7/630 + u**6/540 - u**5/180 + 5*u**3/3 - 2. Let i(l) be the third derivative of n(l). Suppose i(f) = 0. What is f?
-1, 0, 1/2
Let r(v) be the second derivative of -1/70*v**5 + 0*v**3 + 0 + 0*v**2 + 0*v**4 - 4*v. Let r(p) = 0. Calculate p.
0
Let r(i) = -5 + i**2 - i + 2*i**3 - i**3 + 16. Let w be r(0). Factor w*g - 7*g**5 + 15*g**2 - 6*g**2 - 16*g**4 - 4*g**3 + 2 + 5*g**2.
-(g - 1)*(g + 1)**3*(7*g + 2)
Let x be ((-16)/(-24))/((-4)/30). Let b be x/(-6)*(-4)/(-5). Factor 4/3 + b*j - 2/3*j**2.
-2*(j - 2)*(j + 1)/3
Let i(l) = -11*l**4 + 120*l**3 - 231*l**2 + 151*l. Let n(z) = -3*z**4 + 30*z**3 - 58*z**2 + 38*z. Let g(k) = -2*i(k) + 9*n(k). What is o in g(o) = 0?
0, 2
Suppose -z - 3*i = -2, 2*i - 11 = -5*z - 1. Factor 4 - u**z - 3*u**2 + 6*u**2 + 3*u - 9*u.
2*(u - 2)*(u - 1)
Suppose -4*s + h = -1, 4 = -2*s - h + 3. Factor 0*c + 3/5 + s*c**3 - 6/5*c**2 + 3/5*c**4.
3*(c - 1)**2*(c + 1)**2/5
Let q be (2 - (-122)/(-60))*55/(-22). Let b(r) be the second derivative of 1/4*r**2 + q*r**3 + 0 - 1/40*r**5 + 3*r - 1/24*r**4. Find j such that b(j) = 0.
-1, 1
Let d be (11/(-4) + 1)*16/(-112). Factor d*n**2 + 1/4 - 1/2*n.
(n - 1)**2/4
Let c(k) = k**2 - 9*k + 8. Let r be c(8). Let i be (-10)/12*4/(-5). Factor -2/3*q**2 + r*q + i.
-2*(q - 1)*(q + 1)/3
Let k(u) = 3*u**5 - 6*u**3 + 3*u**2 - 3. Let n(w) = -3*w**5 - w**4 + 6*w**3 - 2*w**2 + w + 3. Let h(a) = 4*k(a) + 3*n(a). What is j in h(j) = 0?
-1, 1
Let u(p) be the first derivative of 0*p + 1/48*p**4 + 0*p**3 + 2*p**2 + 2 - 1/240*p**5. Let h(t) be the second derivative of u(t). Factor h(y).
-y*(y - 2)/4
Suppose -5*a = -8*a + 6. Suppose 2*u**a - 5*u**2 + u**2 - 32 - 16*u = 0. What is u?
-4
Let -8/9 - 10/9*a**4 - 16/9*a + 16/9*a**3 + 2*a**2 = 0. Calculate a.
-1, -2/5, 1, 2
Let q(l) be the first derivative of -3*l**5/5 + 15*l**4/4 - 9*l**3 + 21*l**2/2 - 6*l + 13. Factor q(s).
-3*(s - 2)*(s - 1)**3
Let s(o) be the first derivative of -1/24*o**4 + 1/6*o**3 + 0*o**2 - 3 + 0*o. Factor s(y).
-y**2*(y - 3)/6
Suppose 1 = c - 3. Factor 5*q**2 + c + 2*q - 4 + 0*q.
q*(5*q + 2)
Let u = -15828988/605 + 26164. Let m = u + 2/121. Factor 0 + 4/5*s**2 - 2/5*s - m*s**3.
-2*s*(s - 1)**2/5
Suppose 0*y**3 + 0*y + 0*y**2 + 0 + 2/5*y**4 = 0. Calculate y.
0
Let w(j) be the second derivative of 3*j + 3/8*j**4 + 0 - 1/6*j**3 + 0*j**2. Factor w(h).
h*(9*h - 2)/2
Let k(q) be the first derivative of q**4/10 + 2*q**3/5 - 8*q/5 + 20. Factor k(f).
2*(f - 1)*(f + 2)**2/5
Let j be 6/(-4)*(-8)/6. Suppose 2*b = 6 - j. Factor -w**5 + 3*w**3 + b*w**3 + 0*w**5 + 2*w**4 - 6*w**3.
-w**3*(w - 1)**2
Factor -2/3*a**5 + 2/3*a**2 - 2/3*a**4 + 10/3*a**3 + 8/3 - 16/3*a.
-2*(a - 1)**3*(a + 2)**2/3
Suppose -8*k - 5 = -13. Let c(g) be the first derivative of 2*g**2 + 1/2*g**4 - k + 0*g + 2*g**3. Factor c(h).
2*h*(h + 1)*(h + 2)
Determine p, given that -15*p + 39/7*p**2 - 21 - 3/7*p**3 = 0.
-1, 7
Factor -21/5*m + 21/5*m**3 - 9/5 + 9/5*m**2.
3*(m - 1)*(m + 1)*(7*m + 3)/5
Let q(j) = -36*j**3 - 36*j**2 - 24*j + 21. Let b(f) = -f**3 - f + 1. Let h be (3 + 0)/(3 + 0). Let x(d) = h*q(d) - 15*b(d). Factor x(u).
-3*(u + 1)**2*(7*u - 2)
Let i(o) = -o**4 - o**3. Let q(g) = 2*g**4 - 7*g**3 - 33*g**2 - 40*g - 16. Let r(a) = -3*i(a) - q(a). Factor r(x).
(x + 1)**2*(x + 4)**2
Suppose -5*z + z = -20. Suppose -z = p - 6. Solve -4*w - p - 7/4*w**2 = 0 for w.
-2, -2/7
Suppose j - 3 - 1 = y, 16 = 4*j + 2*y. Suppose j*t + n = -3*n + 32, -n = -5. Factor d**4 - d**t - 2*d + 2*d + 0*d**4.
d**3*(d - 1)
Let u(g) = 3*g**3 - 6*g**2 - 12*g + 30. Let v(s) = -1. Let j(p) = -u(p) - 6*v(p). Factor j(z).
-3*(z - 2)**2*(z + 2)
Let a be 7 + -4 + (1 - -1). Let g be ((-3)/a)/(5/(-10)). Suppose 6/5*t + 2/5 + g*t**2 + 2/5*t**3 = 0. What is t?
-1
Let z(b) be the first derivative of -b**4/2 - 2*b**