, 1
Let l(v) = -4*v**2 + 50*v + 12. Let y(a) = -3*a**2 + 51*a + 26. Let z(b) = -2*l(b) + 3*y(b). Suppose z(g) = 0. What is g?
-1, 54
Let d(x) be the second derivative of 1/5*x**3 + 2/5*x**2 + 0 + 1/30*x**4 + x. Factor d(u).
2*(u + 1)*(u + 2)/5
Let q(c) be the first derivative of c**4/14 + c**3/3 - 2*c**2/7 - 71. Factor q(m).
m*(m + 4)*(2*m - 1)/7
Find q such that 2/21*q**2 + 12/7 - 38/21*q = 0.
1, 18
Let s(y) be the third derivative of y**7/105 + 13*y**6/60 + 16*y**5/15 + 5*y**4/3 + 6*y**2 - 7*y. Factor s(b).
2*b*(b + 1)*(b + 2)*(b + 10)
Let a(i) be the first derivative of 3*i**5/25 - 63*i**4/5 + 33*i**3 - 123*i**2/5 - 518. Factor a(b).
3*b*(b - 82)*(b - 1)**2/5
Let v(a) be the third derivative of -a**5/36 - 35*a**4/72 - 25*a**3/9 + 18*a**2 - 3*a. Factor v(h).
-5*(h + 2)*(h + 5)/3
Let m(u) = -u**2 - 139*u - 859. Let c(l) = 69*l + 429. Let s(z) = 5*c(z) + 3*m(z). Let s(r) = 0. Calculate r.
-12
Let -u**2 + 1/6*u**3 - 2/3*u + 4/3 + 1/6*u**4 = 0. What is u?
-2, 1, 2
Let i(p) = p**4 - 7*p**3 - 14*p**2 - 3*p + 3. Let y(c) = -c**4 + 15*c**3 + 28*c**2 + 7*c - 5. Let b(w) = 5*i(w) + 3*y(w). Factor b(x).
2*x*(x + 1)**2*(x + 3)
Let u = -280/71 + 982/213. Solve 4/3*a**2 + 0 - 2/3*a - u*a**3 = 0.
0, 1
Let j(k) be the first derivative of -k**4/4 - k**3/3 + k**2/2 + k + 55. Factor j(c).
-(c - 1)*(c + 1)**2
Let q(t) be the third derivative of t**8/40320 + t**7/10080 + 29*t**5/60 + 8*t**2. Let n(m) be the third derivative of q(m). Find x, given that n(x) = 0.
-1, 0
Let q(m) be the third derivative of -m**7/4620 - m**6/495 - m**5/132 - m**4/66 + 16*m**3/3 - 17*m**2. Let i(c) be the first derivative of q(c). Factor i(x).
-2*(x + 1)**2*(x + 2)/11
Let i(t) be the first derivative of t**3 + 165*t**2 + 327*t + 373. Solve i(o) = 0.
-109, -1
Let f(t) be the first derivative of -2*t**3/63 - 4*t**2/7 - 22*t/21 - 72. Factor f(d).
-2*(d + 1)*(d + 11)/21
Let l be 4/(-42) + (-9988)/(-101640). Let w(i) be the third derivative of 1/132*i**4 + 0*i + 0 + l*i**5 - 2/33*i**3 - 3*i**2. Suppose w(p) = 0. Calculate p.
-2, 1
Let s(g) be the second derivative of g**6/72 - g**5/4 + 15*g**4/8 - g**3/3 + 25*g. Let o(r) be the second derivative of s(r). Factor o(f).
5*(f - 3)**2
Let w = 48448 + -3633491/75. Let q = -3/25 + w. Factor 0*u**3 + 0 + 4/3*u**4 - q*u**2 - 2/3*u**5 + 2/3*u.
-2*u*(u - 1)**3*(u + 1)/3
Suppose -40*h = -36*h - 16. Let x(y) be the first derivative of 2/11*y**3 + 8 + 4/11*y - 2/55*y**5 + 1/22*y**h - 5/11*y**2. Factor x(i).
-2*(i - 1)**3*(i + 2)/11
Let f be (-3 - (-28)/4) + (0 - -2 - 4). Solve -3/7 - 1/7*p**f + 5/7*p - 1/7*p**3 = 0.
-3, 1
Factor 5/2 - 1/6*k**2 - 7/3*k.
-(k - 1)*(k + 15)/6
Let w(r) be the first derivative of -r**3/5 + 69*r**2/10 - 54*r - 899. Factor w(o).
-3*(o - 18)*(o - 5)/5
Find m such that 6/5 - 13/5*m**2 + 19/5*m + 7/5*m**4 - 19/5*m**3 = 0.
-1, -2/7, 1, 3
Let f(x) be the second derivative of x**5/20 - 3*x**4/8 + x**3 + x**2 + 4*x. Let s(d) be the first derivative of f(d). Let s(g) = 0. Calculate g.
1, 2
Let u(z) be the third derivative of z**6/540 - 13*z**5/135 + 169*z**4/108 + 47*z**2. Factor u(f).
2*f*(f - 13)**2/9
Suppose 3*v - 10 = 4*q - 3*q, 0 = 2*v - 8. Let y(i) be the first derivative of 5 - 2/9*i**q - 1/18*i**4 - 2/9*i**3 + 0*i. Let y(a) = 0. Calculate a.
-2, -1, 0
What is f in 0 + 2/7*f**3 - 6*f**2 - 92/7*f = 0?
-2, 0, 23
Let a = -23 + 37. Suppose a + 370 = 4*l. Factor -h**2 + 5*h**2 - 96*h + 2*h**3 + l*h.
2*h**2*(h + 2)
Suppose 21 = l + 19. Let h(n) be the first derivative of 3 - 8*n**l + 0*n - 4/3*n**3. Solve h(a) = 0 for a.
-4, 0
Let t(f) be the first derivative of -2*f**3/3 - 7*f**2 + 156*f - 428. Factor t(a).
-2*(a - 6)*(a + 13)
Suppose 11*o = 7*o - 5*o. Factor -2/13*u**5 + 0*u + o + 2/13*u**2 + 2/13*u**3 - 2/13*u**4.
-2*u**2*(u - 1)*(u + 1)**2/13
Suppose 4*i - 14 = -6. Let h(b) be the second derivative of 0*b**3 + 3/20*b**5 + 1/4*b**4 + 0*b**i + 0 - 2*b. Find o, given that h(o) = 0.
-1, 0
Suppose 0 = 9*g - 1101 + 1083. Let m(l) be the second derivative of 0 + 9*l + 1/36*l**4 + 0*l**g + 0*l**3 + 1/60*l**5. Factor m(r).
r**2*(r + 1)/3
Let i be (-1)/6 - (-112)/96. Let k = -2926 - -8779/3. Factor i + 2/3*u - k*u**2.
-(u - 3)*(u + 1)/3
Suppose h = -9*h + 20. Suppose -3 - 5 = -4*n. Solve -166*r + n*r**h - 2 + 166*r = 0.
-1, 1
Let p(x) = -x + 10. Let v be p(10). Suppose 4*q = -v*q + 32. Find i such that -16*i + q*i + 5*i + 3*i**3 = 0.
-1, 0, 1
Let c = 23 + -21. Suppose 0*o = -c*o + 4. Let l + 2*l**o + 0*l**2 + 32*l**4 + 0*l + 2 - 13*l + 48*l**3 = 0. Calculate l.
-1, 1/4
Let p(s) be the second derivative of s**4/114 - s**3/19 + 2*s**2/19 - 77*s. Find z such that p(z) = 0.
1, 2
Suppose -35 = -20*d + 2*d + 19. Let o(z) = z**2 + 4*z + 2. Let s be o(-4). Factor -1/5*v**5 + 0 + 0*v**d + 2/5*v**4 + 0*v + 0*v**s.
-v**4*(v - 2)/5
Let i be (-1)/(-4)*12 + 0. Let n(o) be the first derivative of 2 + 1/20*o**4 + 1/2*o**2 - 2/5*o - 4/15*o**i. What is h in n(h) = 0?
1, 2
Let x be -2*(-5)/(-10)*2/(-3). Suppose -1/3*o + 2/3*o**2 + x*o**3 - 1/3*o**5 - 1/3*o**4 - 1/3 = 0. Calculate o.
-1, 1
Let b be 3*(-1 - -6)*(-3)/(-15). Let q(w) be the second derivative of 0*w**2 - 1/120*w**6 + 0*w**b + 5*w + 0 + 0*w**4 - 1/80*w**5. Factor q(f).
-f**3*(f + 1)/4
Let d(c) be the first derivative of 3*c**5/5 + 33*c**4/4 - 25*c**3 + 39*c**2/2 - 58. Factor d(r).
3*r*(r - 1)**2*(r + 13)
Suppose -14*r + 10*r - 28 = 0. Let w(x) = -6*x - 37. Let s be w(r). Solve -1/4 + 3/4*k**4 - 1/2*k**3 + 3/4*k - 1/4*k**s - 1/2*k**2 = 0.
-1, 1
Suppose 6*r = 41941 - 41929. Suppose -1/2*a**r - 9/2 - 3*a = 0. Calculate a.
-3
Factor 196*k + 3*k**2 + 185*k - 399*k - 48.
3*(k - 8)*(k + 2)
Let j = -26 + 30. Let -127*o**3 + 20*o**5 - 5*o**2 - 25*o**j + 30*o**2 - 5*o + 112*o**3 = 0. Calculate o.
-1, 0, 1/4, 1
Let h(g) = -35*g**3 + 820*g**2 + 40600*g + 703020. Let b(k) = -2*k**3 + 2*k**2 + 2*k - 1. Let n(v) = 20*b(v) - h(v). Solve n(s) = 0 for s.
-52
Factor 34/3*c**2 - 2/3*c**3 + 38/3 + 74/3*c.
-2*(c - 19)*(c + 1)**2/3
Suppose 2*l + 2*k = -0*l + 114, 0 = 4*l + 2*k - 226. Factor -l*t + 92*t**2 - 301*t**3 - 10 - 10 + 285*t**3.
-4*(t - 5)*(t - 1)*(4*t + 1)
Let u = 11890/76947 + -4/5919. What is l in -u*l**2 + 2/13*l + 4/13 = 0?
-1, 2
Suppose x = 4*m + 165, -x = 2*x - 15. Let p be 9/((-5)/(m/12)). Let 15*h**2 - 15*h**4 + 3*h - 6*h + p*h**5 + 0*h - 3*h = 0. Calculate h.
-1, 0, 1/2, 1, 2
Let w = 187 - -16. Let l = w + -201. Factor 0 - 1/2*j**4 + l*j + 0*j**2 - 3/2*j**3.
-j*(j - 1)*(j + 2)**2/2
Let k be 98/48 - 7*8/28. Let i(l) be the second derivative of -1/4*l**3 + 3*l + k*l**4 + 1/2*l**2 + 0. What is c in i(c) = 0?
1, 2
Let f(t) be the second derivative of -t**5/40 - t**4/2 + 13*t**3/12 + 9*t - 11. Suppose f(o) = 0. What is o?
-13, 0, 1
Factor 91*r**4 + 4*r - 5*r - 95*r**4 - 4 + r + 8*r**2.
-4*(r - 1)**2*(r + 1)**2
Let c(b) be the first derivative of -b**5/30 - 73*b**4/24 + 38*b**3/3 - b**2/3 - 152*b/3 + 252. Determine s so that c(s) = 0.
-76, -1, 2
Let p(c) be the first derivative of -c**3/21 + 27*c**2/14 - 72*c/7 + 147. Factor p(r).
-(r - 24)*(r - 3)/7
Let q(b) be the second derivative of b**6/75 - 3*b**5/50 - b**4/30 + b**3/5 + 4*b + 14. Solve q(s) = 0 for s.
-1, 0, 1, 3
Let s be 29/(-319) + (-94)/(-66). Let u(b) be the first derivative of s*b**3 - 4 + 8*b**2 + 12*b. What is q in u(q) = 0?
-3, -1
Let p be ((-14)/(-18) - 1) + 820/369. Let l = -66 - -66. Determine o, given that -1/2*o**p + l + 1/4*o + 1/4*o**3 = 0.
0, 1
Solve 0*q + 0 - 1/3*q**4 - 53/3*q**3 - 52/3*q**2 = 0.
-52, -1, 0
Factor -32/11*j + 2/11*j**2 + 0.
2*j*(j - 16)/11
Let r = 126 + -123. Find u such that 14*u**r + 13*u**3 - 15*u**2 - 10*u + 22*u**3 + 11*u**3 - 35*u**4 = 0.
-2/7, 0, 1
Let w(g) be the third derivative of g**6/240 + g**5/60 - g**4/2 + 2*g**2 - 18*g. Factor w(i).
i*(i - 4)*(i + 6)/2
Let n = 97 - 112. Let d be -2 + (6/n)/((-4)/20). Find i, given that 0*i + 0*i**2 + d + 2/7*i**3 = 0.
0
Let k = -30 - -31. Let q(t) = t**2 + 5*t - 2. Let i(v) = v**2 - v + 1. Let d(y) = k*q(y) - 4*i(y). Suppose d(o) = 0. Calculate o.
1, 2
Let m(f) = -64*f**2 - 39*f - 6. Let j(p) = 220*p**2 + 42 + 20*p**2 + 207*p**2 + 273*p. Let g(a) = 4*j(a) + 27*m(a). Find l, given that g(l) = 0.
-2/5, -1/4
Let d = -25/4 - -19/4. Let z = d + 2. Factor 1 - 1/2*i - i**2 + z*i**3.
(i - 2)*(i - 1)*(i + 1)/2
Let o(a) = 4*a + 38. Let d be o(-9). Factor -3*i**3 + 0*i**2 - 3*