
5*a**2*(a + 159)**2
Let o(z) be the second derivative of z**5/20 - 5*z**4/6 + 3*z**3/2 + z**2 - 6*z. Let t be o(9). Suppose -1 - 4*h**2 + 3 - 2 - 2*h**3 + t*h**4 = 0. Calculate h.
-1, 0, 2
Let p(o) be the second derivative of -7*o**5/8 + 47*o**4/12 - 13*o**3/3 + 2*o**2 + 3*o + 56. Factor p(r).
-(r - 2)*(5*r - 2)*(7*r - 2)/2
Let s(g) be the third derivative of g**6/600 + g**5/15 + 37*g**4/120 + 3*g**3/5 - 34*g**2 + 3*g. Factor s(t).
(t + 1)**2*(t + 18)/5
Let n(h) = -h**2 - 23*h + 54. Let l be n(-25). Let m(g) be the first derivative of 4 - 1/5*g**5 + g**3 - 2*g**2 + 1/2*g**4 - l*g. Factor m(p).
-(p - 2)**2*(p + 1)**2
Let r = -19 - -20. Factor 89*v + 2*v**2 - r + 1 - 91*v.
2*v*(v - 1)
Let y(h) be the third derivative of -25/12*h**4 + 20/3*h**3 + 1/6*h**6 + 1/42*h**7 - 1/4*h**5 + 0*h + 16*h**2 + 0. Solve y(n) = 0.
-4, -2, 1
Let m be 4 + 88/(-110) + -12*4/15. Solve m*a**2 - 4/17*a - 2/17*a**4 + 2/17 + 4/17*a**3 = 0.
-1, 1
Let k = -9 - -63. Factor -t**2 + 2*t**2 - 57*t + 2 + k*t.
(t - 2)*(t - 1)
Let c(y) be the third derivative of y**5/480 + 155*y**4/96 + 24025*y**3/48 - 826*y**2. Determine a, given that c(a) = 0.
-155
Let t(g) be the second derivative of -g**7/189 - g**6/135 + g**5/5 - 7*g**4/27 - 17*g**3/27 + 5*g**2/3 - 195*g. Solve t(j) = 0 for j.
-5, -1, 1, 3
Let y(l) be the third derivative of -1/36*l**4 - 18*l**2 + 0 + 1/540*l**5 + 1/6*l**3 + 0*l. Solve y(f) = 0 for f.
3
Let x(j) = -j**2 - j - 1. Let p(k) = -k + 3*k**2 - 2*k**2 + 2*k**2 - 2*k - 1. Suppose q - 2*q = -5. Let a(m) = q*x(m) + p(m). Suppose a(y) = 0. Calculate y.
-3, -1
Let m(u) be the third derivative of 0*u**4 - 1/90*u**6 + 0*u + 0*u**3 + 0 - 2/315*u**7 + 1/252*u**8 + 5*u**2 + 1/45*u**5. Find z, given that m(z) = 0.
-1, 0, 1
Let s be (-18)/12*-1*4892/6. Factor k**2 + s - 1223 - 4*k.
k*(k - 4)
Let u(i) be the third derivative of -i**6/120 - 3*i**5/10 - 9*i**4/2 - 37*i**3/6 - 37*i**2. Let o(v) be the first derivative of u(v). Factor o(g).
-3*(g + 6)**2
Let m(h) be the first derivative of h**4/32 + 9*h**3/16 - 15*h**2/8 - 10*h + 37. Let p(l) be the first derivative of m(l). Suppose p(x) = 0. Calculate x.
-10, 1
Let w(u) = 3*u**5 + u**4 - 12*u**3 + 10*u**2. Let z(n) = 4*n**5 + 2*n**4 - 14*n**3 + 9*n**2. Let c(q) = 3*w(q) - 2*z(q). Factor c(d).
d**2*(d - 2)**2*(d + 3)
Factor -40/3*h**3 + 0 - 32/3*h**2 + 0*h - 16/3*h**4 - 2/3*h**5.
-2*h**2*(h + 2)**2*(h + 4)/3
Let h(f) be the second derivative of f**5/60 + 31*f**4/36 + 43*f**3/9 + 28*f**2/3 + f - 86. Find y, given that h(y) = 0.
-28, -2, -1
Solve 14 + 20/3*q + 2/3*q**2 = 0.
-7, -3
Let t be (-5)/25 - (-3)/15. Let q(a) be the first derivative of 0*a + t*a**4 - a**3 + 1 + 1/5*a**5 + a**2. Find o, given that q(o) = 0.
-2, 0, 1
Let z = -60 - -65. Solve -z*p**2 + 80*p**3 + 13*p**2 + 65*p**2 + 11*p**2 + 16*p = 0 for p.
-4/5, -1/4, 0
Let w(q) be the third derivative of -q**6/40 + 3*q**5/4 - 63*q**4/8 + 49*q**3/2 - 75*q**2. Suppose w(o) = 0. What is o?
1, 7
Factor 48*k - 128 - 13 - 143 + 3*k**2 + 44.
3*(k - 4)*(k + 20)
Let h(s) be the second derivative of s**6/90 - 7*s**5/60 - 5*s**4/18 + 8*s**3/9 + 155*s - 2. Solve h(j) = 0.
-2, 0, 1, 8
Let k(f) be the second derivative of f**7/336 - 17*f**6/240 + 9*f**5/32 - 43*f**4/96 + 7*f**3/24 - 61*f. Factor k(a).
a*(a - 14)*(a - 1)**3/8
Let j(o) be the third derivative of o**8/110880 + o**7/27720 + 4*o**5/15 + 12*o**2. Let u(k) be the third derivative of j(k). Factor u(g).
2*g*(g + 1)/11
Let o(f) be the third derivative of f**9/2016 - 3*f**8/560 + 9*f**7/560 + 6*f**3 + 9*f**2. Let v(y) be the first derivative of o(y). Factor v(r).
3*r**3*(r - 3)**2/2
Let k = -4 - -7. Let q(v) = v**2 + v**2 + 5*v**3 + k*v - v**3. Let i(f) = 5*f**3 + 3*f**2 + 4*f. Let h(n) = -3*i(n) + 4*q(n). Let h(c) = 0. What is c?
0, 1
Let a = 18989/7 - 2711. Factor -3/7*y**3 - a*y + 11/7*y**2 + 4/7.
-(y - 2)*(y - 1)*(3*y - 2)/7
Let r(k) = k**3 + 14*k**2 + 67*k + 518. Let t be r(-12). Factor -2/7*p**t - 10/7 + 12/7*p.
-2*(p - 5)*(p - 1)/7
Let b(t) be the third derivative of t**5/20 - t**3/2 + 124*t**2. Let b(k) = 0. Calculate k.
-1, 1
Let s(d) be the third derivative of -d**5/15 - 13*d**4/6 - 20*d**3 - 13*d**2 - 5*d. Factor s(o).
-4*(o + 3)*(o + 10)
Let h(l) be the second derivative of -l**6/20 + 9*l**5/20 - 9*l**4/8 + l**3 - 4*l + 1. Let h(p) = 0. Calculate p.
0, 1, 4
Let r be 2/17 + 2400/8500. Let -r*w**3 - 4/5*w - 6/5*w**2 + 0 = 0. What is w?
-2, -1, 0
Let b(w) be the second derivative of 2*w**7/35 - w**6/6 - w**5/15 + 5*w**4/6 - 4*w**3/3 - w**2/2 + 13*w. Let z(h) be the first derivative of b(h). Factor z(s).
4*(s - 1)**2*(s + 1)*(3*s - 2)
Factor 18/7*j**2 + 2/21*j**3 + 338/21 + 130/7*j.
2*(j + 1)*(j + 13)**2/21
Suppose -25*o + 5 + 14 = -31. Suppose 16/15*m + 2/15*m**3 + 2/3*m**o + 8/15 = 0. Calculate m.
-2, -1
Suppose 3*j - 10*j + 70 = 0. Factor -90*q - 77 + 482 - q**2 + j*q**2 - 4*q**2.
5*(q - 9)**2
Let c = 8143/5 - 1628. Factor 0*b**2 + 6/5*b - c - 6/5*b**3 + 3/5*b**4.
3*(b - 1)**3*(b + 1)/5
Let c = -5/4 - -21/16. Let k(r) be the first derivative of -c*r**4 + 1/4*r - 1 - 1/12*r**3 + 1/8*r**2. Factor k(w).
-(w - 1)*(w + 1)**2/4
Let t = 12 - -19. Let w = -154/5 + t. Let 2/5*n + 1/5*n**2 + w = 0. Calculate n.
-1
Let x = 2299 + -2297. What is j in 2*j**3 - x*j - 3/2*j**2 + 2 - 1/2*j**4 = 0?
-1, 1, 2
Let f(h) be the third derivative of -h**6/480 + h**5/48 + 17*h**4/96 - 7*h**3/8 - h**2 - 1. Factor f(i).
-(i - 7)*(i - 1)*(i + 3)/4
Let r(w) be the third derivative of w**8/5040 - w**7/315 + w**6/60 - 3*w**5/4 - 20*w**2. Let t(s) be the third derivative of r(s). Determine k so that t(k) = 0.
1, 3
Let d(t) be the first derivative of -5*t**3/6 - 75*t**2/2 - 45. Find i, given that d(i) = 0.
-30, 0
Let g(q) be the first derivative of -q**4/2 + 34*q**3/3 - 70*q**2 + 449. Let g(a) = 0. Calculate a.
0, 7, 10
Find o such that 2/3*o**4 + 0*o**2 + 4/3*o**3 + 0 + 0*o = 0.
-2, 0
Factor -113*v - 1/2*v**2 - 12769/2.
-(v + 113)**2/2
Suppose 4*x - 9 = x. Factor 21*a**3 - x*a + 3 - 32*a**3 - 3*a**2 + 14*a**3.
3*(a - 1)**2*(a + 1)
Let m(z) be the second derivative of 1/5*z**5 + 0 + 22*z + 0*z**3 + 1/3*z**4 + 0*z**2 - 2/21*z**7 - 2/15*z**6. Factor m(i).
-4*i**2*(i - 1)*(i + 1)**2
Suppose 0 = -t - 2*t + 72. Determine v, given that -17*v**2 + 8*v**3 - 4*v**4 - 8*v - t*v**3 - 3*v**2 = 0.
-2, -1, 0
Let d = 5481/4 - 1369. Determine x, given that 1/2 + x**2 + d*x + 1/4*x**3 = 0.
-2, -1
Let c = 32 - 28. What is m in -m**4 + 2*m**c - 3*m**4 + 4*m**2 + 2*m**3 - 4*m**4 = 0?
-2/3, 0, 1
Suppose -16/15 - 2/15*d**3 - 4/3*d**2 - 34/15*d = 0. What is d?
-8, -1
Let h(b) = -36*b**2 - 25*b - 1. Suppose -3*i + 5*i + 10 = 0, 2*k - 4*i = 8. Let f(u) = -71*u**2 - 50*u - 1. Let t(q) = k*f(q) + 11*h(q). Factor t(v).
5*(v + 1)*(6*v - 1)
Let r(u) be the first derivative of u**3/15 - u**2/10 - 12*u/5 + 172. Let r(i) = 0. What is i?
-3, 4
Let x(h) = 2. Let t(w) = -w**2 + 60*w - 894. Let z(m) = 2*t(m) - 6*x(m). Factor z(g).
-2*(g - 30)**2
Let q(g) be the second derivative of -g**7/42 - 2*g**6/15 + 39*g**5/10 - 18*g**4 + 9*g**3/2 + 162*g**2 - 270*g. Factor q(n).
-(n - 3)**3*(n + 1)*(n + 12)
Let t(u) be the first derivative of 2/3*u**3 + 1/6*u**4 + 0*u - 4/3*u**2 - 8. Determine h, given that t(h) = 0.
-4, 0, 1
Let f(i) be the second derivative of i**5/5 + 23*i**4/3 + 160*i**3/3 + 152*i**2 + 66*i + 2. Let f(x) = 0. What is x?
-19, -2
Let v(t) = -2*t**2 - 146*t - 27. Let k(n) = n**2 + 68*n + 13. Let z(u) = -13*k(u) - 6*v(u). Determine h, given that z(h) = 0.
-7, -1
Let x(t) be the third derivative of -t**5/15 - 3*t**4/2 - 28*t**2. Factor x(l).
-4*l*(l + 9)
Let v = 23 - 13. Let u(z) = z**2 + 5 - v*z**2 - 6*z**2 + 4*z**3. Let p(f) = -5*f**3 + 14*f**2 - f - 4. Let h(j) = -3*p(j) - 2*u(j). Find d, given that h(d) = 0.
-2/7, 1
Let c(d) = 5*d**3 + 184*d**2 + 179*d - 6. Let g(o) = 70*o**3 + 2575*o**2 + 2505*o - 85. Let i(a) = 85*c(a) - 6*g(a). Let i(t) = 0. Calculate t.
-37, -1, 0
Suppose 8*x + 10*x - 81*x = -126. Determine u, given that -4/7*u + 8/7 - 4/7*u**x = 0.
-2, 1
Let 6/5*w + 2/5*w**2 + 0 = 0. What is w?
-3, 0
Let w be ((-3 - -2)/(-1) - -17)/2. Factor -35*i - w + 8*i + 21*i + 3*i**2.
3*(i - 3)*(i + 1)
Find f, given that 12/5*f - 9/5*f**3 - 3/5*f**5 + 3*f**2 - 3*f**4 + 0 = 0.
-4, -1, 0, 1
Let z = 10297 - 10295. Factor -6*m + 1/2*m**z + 18.
(m - 6)**2/2
Suppose w - 37 - 63 = 0. Let y =