
Let f(l) = 2*l**3 - 2*l**2 + 3*l. Let g be f(2). Let i = g + -11. Solve i*o**3 - 3*o**3 - 2*o**3 = 0 for o.
0
Let y(k) be the first derivative of -2*k**3/3 - 6*k**2 - 16*k - 269. Let y(l) = 0. Calculate l.
-4, -2
Suppose 0 = 15*h + 18*h - 10*h. Factor 0 + h*x**2 - 1/8*x**3 + 1/8*x.
-x*(x - 1)*(x + 1)/8
Let m be (3 + -4)*24/(-3). Determine v so that -2*v**5 + 2*v**3 - 48*v - m*v**3 + 12*v**4 - 44*v**2 - 16 + 2*v**3 + 6*v**5 = 0.
-2, -1, 2
Let g(d) be the first derivative of -8 + 0*d**3 + 2/65*d**5 - 1/26*d**4 + 0*d**2 + 0*d. What is q in g(q) = 0?
0, 1
Let u(v) be the third derivative of v**7/735 - 2*v**6/21 + 157*v**5/70 - 117*v**4/7 + 324*v**3/7 + 237*v**2. Find r such that u(r) = 0.
1, 3, 18
Let m(u) be the first derivative of -u**5/5 + 7*u**4/8 - 7*u**3/6 + u**2/2 + 233. Factor m(b).
-b*(b - 2)*(b - 1)*(2*b - 1)/2
Factor 0*b**3 + 16/5*b - 1/5*b**5 + 16/5*b**2 + 0 - 4/5*b**4.
-b*(b - 2)*(b + 2)**3/5
Let l(s) be the first derivative of 5/4*s**2 - 1/6*s**3 + 6 + 0*s. Factor l(z).
-z*(z - 5)/2
Factor w**2 + 8*w + 9*w**2 - 12*w**2.
-2*w*(w - 4)
Suppose 428*q = 432*q. Let z(n) be the third derivative of -3/40*n**6 - 9/20*n**5 + 0*n - 1/210*n**7 - n**2 + q*n**3 - 9/8*n**4 + 0. Let z(s) = 0. What is s?
-3, 0
Suppose 2*k = -k + 72. Suppose -3*j + k = 3. Let d(m) = 3*m**2 + 5*m + 2. Let t(p) = -4*p**2 - 7*p - 3. Let q(u) = j*d(u) + 5*t(u). Factor q(f).
(f - 1)*(f + 1)
Let j(p) = -4*p**4 - 57*p**3 - 288*p**2 - 445*p. Let o(w) = -4*w**4 - 58*w**3 - 288*w**2 - 446*w. Let m(v) = -2*j(v) + 3*o(v). Factor m(t).
-4*t*(t + 4)**2*(t + 7)
Suppose -6 = -h - 1. Suppose -h*v - 5*c + 30 = 0, 4*v = 2*c + c + 3. Find q such that 1 + 0 + v*q - q**3 + 0 - 3 = 0.
-2, 1
Let z(f) be the second derivative of 0 + 1/1980*f**6 + 2*f + 0*f**2 + 5/6*f**3 - 1/660*f**5 + 0*f**4. Let b(m) be the second derivative of z(m). Solve b(w) = 0.
0, 1
Let u(f) be the first derivative of f**4/28 - 20*f**3/7 - 123*f**2/14 - 62*f/7 - 498. Factor u(o).
(o - 62)*(o + 1)**2/7
Suppose 9 = 53*c - 1 + 10. Find p such that 0 + 2/3*p**4 - 2/3*p**3 - 2/3*p**2 + 2/3*p**5 + c*p = 0.
-1, 0, 1
Let p(j) = -2*j. Let y(c) = -144*c**2 - 54*c - 4. Let t(q) = -3*p(q) + y(q). Determine k so that t(k) = 0.
-1/6
Let p(d) be the second derivative of d**7/1260 - d**6/180 + d**5/60 - d**4/2 - 2*d. Let s(a) be the third derivative of p(a). Find m, given that s(m) = 0.
1
Suppose 7*i - 4 = 5*i. Let t be i - (-9 + 12)*(-2)/6. Factor -u**t + u + 1/3*u**4 - 2/3 + 1/3*u**2.
(u - 2)*(u - 1)**2*(u + 1)/3
Let o(t) = 21*t - 479. Let w be o(23). Determine z so that -2*z**3 - 6*z**2 - 6*z + 0 - 2/9*z**w = 0.
-3, 0
Let t(d) = -10*d + 33. Let s be t(3). Let n be ((-8)/3)/8*s - -3. Suppose -6/7*k - 2/7 + 6/7*k**4 - 4/7*k**n + 4/7*k**3 + 2/7*k**5 = 0. Calculate k.
-1, 1
Let x(m) = 3*m**4 + 40*m**3 + 57*m**2 - 12*m - 32. Let c(s) = -s**4 - 20*s**3 - 29*s**2 + 6*s + 16. Let t(p) = -9*c(p) - 4*x(p). Factor t(q).
-(q - 8)*(q + 1)**2*(3*q - 2)
Let h(q) be the third derivative of -q**8/96 + 71*q**7/280 + 113*q**6/80 + 107*q**5/60 + 3*q**4/4 + 205*q**2. Suppose h(y) = 0. Calculate y.
-2, -1/2, -2/7, 0, 18
Let z(u) be the first derivative of 81*u**4/8 + 19*u**3 + 35*u**2/4 + u - 2. Factor z(i).
(i + 1)*(3*i + 1)*(27*i + 2)/2
Let w(v) be the second derivative of 0 - 31*v - 1/90*v**4 + 0*v**2 - 1/45*v**3. Suppose w(m) = 0. What is m?
-1, 0
Let u = 20 + -27. Let c = u + 25. Let -3*s**4 + c*s**3 - 7*s + 32*s**4 - 10*s**2 - 1 - 27*s**5 - 2*s**4 = 0. What is s?
-1/3, 1
Let s(g) = g**3 + g**2 + g. Let t(p) = 2*p**3 - 18*p**2 + 18*p - 8. Suppose f = -0*f + 10. Let z be 4*(-3 - f/(-4)). Let l(j) = z*s(j) - t(j). Factor l(c).
-4*(c - 2)*(c - 1)**2
Suppose 3*h + 5*k - 14661 = 0, k - 4 = -1. Factor -7*z**2 + 45*z + 4857 - 5*z**3 - h - 8*z**2.
-5*(z - 1)**2*(z + 5)
Let t = 40 - 14. Solve 4*c**4 + 27*c**2 + t*c**2 - 57*c**2 = 0.
-1, 0, 1
Let b = 15 + -7. Suppose -10 = b*c - 13*c. Factor 0*l + 3*l**5 - 2*l**2 - 2*l + 2*l**4 + l - c*l**5.
l*(l - 1)*(l + 1)**3
Let t(r) be the second derivative of -3*r**5/20 + 5*r**4/2 - 9*r**3/2 + r - 252. Factor t(z).
-3*z*(z - 9)*(z - 1)
Let r(t) be the second derivative of -2*t**6/25 - 7*t**5/25 + 13*t**4/15 + 14*t**3/15 - 4*t**2 - 7*t + 18. What is z in r(z) = 0?
-10/3, -1, 1
Factor -24*b + 23 - 4*b**2 - 26 - 29.
-4*(b + 2)*(b + 4)
Factor -26/5*u + 2/5*u**3 + 44/5 - 4*u**2.
2*(u - 11)*(u - 1)*(u + 2)/5
Let h(k) be the second derivative of k**10/7560 - k**8/560 - k**7/315 - k**4/4 - 8*k. Let v(j) be the third derivative of h(j). What is t in v(t) = 0?
-1, 0, 2
Let q(u) be the second derivative of u**7/7560 - u**6/216 + 5*u**5/72 + 5*u**4/6 - 8*u. Let y(h) be the third derivative of q(h). Factor y(m).
(m - 5)**2/3
Let u = 37 + -33. Factor u*z**2 - z**3 - 684*z**4 - z**3 + 682*z**4.
-2*z**2*(z - 1)*(z + 2)
Factor 2*y**2 + 14*y**2 + 6*y**3 + 4*y**4 - 14*y**2.
2*y**2*(y + 1)*(2*y + 1)
Let i(z) be the second derivative of z**4/21 + 6*z**3/7 + 4*z**2 + 52*z. Factor i(f).
4*(f + 2)*(f + 7)/7
Let b(s) be the third derivative of 5*s**8/336 + s**7/7 + s**6/12 - 4*s**5/3 - 5*s**4/8 + 25*s**3/3 + 3*s**2 + 31*s. What is z in b(z) = 0?
-5, -2, -1, 1
Find i such that 0 - 3*i**3 - 5*i**2 - 7/3*i - 1/3*i**4 = 0.
-7, -1, 0
Factor 3*i**5 - 3*i**5 + 3*i**5 - 270*i**2 + 135*i**3 - 8*i**5.
-5*i**2*(i - 3)**2*(i + 6)
Let x(r) be the third derivative of 1/42*r**7 + 5/24*r**6 + 0*r**4 + 0 + 1/3*r**5 + 0*r**3 - 15*r**2 + 0*r. Suppose x(i) = 0. What is i?
-4, -1, 0
Let d(i) be the second derivative of -21*i + 0*i**2 - 1/6*i**3 - 1/96*i**4 + 0. Factor d(l).
-l*(l + 8)/8
Let y = -37 + 43. Let u(d) be the first derivative of 2/3*d**2 - y + 2/3*d + 2/9*d**3. Factor u(s).
2*(s + 1)**2/3
Solve z - 1/3*z**3 - 2/3*z**2 + 0 = 0 for z.
-3, 0, 1
Factor -4*s**4 + 28*s**4 + 17*s**5 - 57*s**3 + 30*s**2 - 14*s**5.
3*s**2*(s - 1)**2*(s + 10)
Let c(h) be the first derivative of -h**5/15 + 8*h**3/3 - h**2/2 + 19. Let k(y) be the second derivative of c(y). Factor k(i).
-4*(i - 2)*(i + 2)
Let w be (-378)/(-8)*(-6)/(-27). Factor w*g + 15/2*g**3 - 3 - 27/2*g**2 - 3/2*g**4.
-3*(g - 2)*(g - 1)**3/2
Let o(y) be the first derivative of 3*y**4/10 + 12*y**3/5 + 252. Let o(n) = 0. What is n?
-6, 0
Let y(s) be the third derivative of -s**5/330 + 13*s**4/132 + 14*s**3/33 + 4*s**2 + 40. Factor y(z).
-2*(z - 14)*(z + 1)/11
Let m = 28501 + -199506/7. Factor m*w**4 + 0 - 3/7*w**3 + 4/7*w + 0*w**2.
w*(w - 2)**2*(w + 1)/7
Let 16*k + 16*k + 3485*k**2 - 3484*k**2 = 0. What is k?
-32, 0
Let p(k) be the first derivative of -37 - 1/2*k - 1/6*k**2 + 1/18*k**3. Factor p(d).
(d - 3)*(d + 1)/6
Let o be -27 - (-21 + (-1300)/170). Factor 16/17*y**2 - 2/17*y**3 - o - 10/17*y.
-2*(y - 7)*(y - 2)*(y + 1)/17
Factor -70*y + 48 + 5*y**3 - 72 - 74 + 45 - 67 + 5*y**2.
5*(y - 4)*(y + 2)*(y + 3)
Let q(t) be the first derivative of -1/7*t**4 + 16/21*t**3 - 4/35*t**5 + 0*t + 8/7*t**2 + 2. Factor q(g).
-4*g*(g - 2)*(g + 1)*(g + 2)/7
Find b, given that -1296/7 + 4/7*b**3 - 148/7*b**2 + 1440/7*b = 0.
1, 18
Let p(a) be the third derivative of a**6/24 - 3*a**5/4 - 85*a**4/12 - 20*a**3 - 436*a**2. Solve p(v) = 0.
-2, -1, 12
Let 33/7*u**3 + 0 + 16/7*u + 1/7*u**5 - 40/7*u**2 - 10/7*u**4 = 0. What is u?
0, 1, 4
What is f in 48*f**3 + 2*f**4 - 2*f**5 + 307 + 0*f**3 + 80*f**2 + f - 403 - 33*f = 0?
-2, 1, 6
Factor 1/6*y**2 + 5/3*y + 3/2.
(y + 1)*(y + 9)/6
Solve 32/21*k**4 - 500/21 + 340/21*k**2 - 2/21*k**5 - 176/21*k**3 + 50/21*k = 0 for k.
-1, 2, 5
Let m(q) be the second derivative of 0 + 10*q + 1/50*q**5 - 1/15*q**3 + 1/5*q**2 - 1/30*q**4. Solve m(a) = 0.
-1, 1
Factor -3*f + 2*f - 4*f**2 + 2*f**5 + 3*f**3 + 4*f**4 - 3*f - f**5.
f*(f - 1)*(f + 1)*(f + 2)**2
Let p = -2725 + 2727. Let 4/3*o + 2/3*o**2 - p = 0. Calculate o.
-3, 1
Let a(g) be the first derivative of -g**6/63 + 2*g**5/5 - 103*g**4/42 + 46*g**3/7 - 184*g**2/21 + 40*g/7 - 467. Suppose a(l) = 0. Calculate l.
1, 2, 15
Let o = -109705/7 - -15673. Suppose -2/7*g**2 - o + 8/7*g = 0. Calculate g.
1, 3
Let b(j) be the third derivative of -j**6/60 + j**5/5 - 3*j**4/4 - 2*j**2 - 56. What is d in b(d) = 0?
0, 3
Let u(q) be the second derivative of 1/4*q**4 - 1/10*q**6 + 0*q**2 + 1/3*q**3 - 1/42*q**7 + 0 - 1/20*q**5 + 18*q. Determine s so that u(s) = 0.
-2, -1, 0, 1
Let h(p) = 29*p**4 - 19*p**3 - 180*p**2 + 319*p - 149. Let q(g) = 14*g**4 - 9*g**3 - 90*g**2 + 15