35*k**5 + 8*k**4 - 8*k**2 + 4*k**3 - 6*k - 32*k**5 = 0.
-3, -1, 0, 1
Let m = 126 - 123. Factor -9/5*y + 6/5*y**m + 3/5 - 9/5*y**4 + 3/5*y**5 + 6/5*y**2.
3*(y - 1)**4*(y + 1)/5
Factor -145*g + 32 + 636*g**2 - 75*g - 148*g + 508*g**2 - 484*g**3.
-4*(g - 2)*(11*g - 2)**2
Let c(g) be the first derivative of 7*g**6/20 + 13*g**5/40 + g**4/12 + 29*g - 13. Let q(w) be the first derivative of c(w). Factor q(r).
r**2*(3*r + 1)*(7*r + 2)/2
Suppose -24 = -2*g + 3*c, 2*g - 10 = -c + 14. Suppose -2*m - 2*m + 8 = 0, 2*x = -4*m + g. Let -3 + 2*k**3 + 3*k**4 + 4*k**3 - 3*k - x*k - k = 0. Calculate k.
-1, 1
Let y(o) be the first derivative of -55*o**4/4 - 80*o**3/3 + 5*o**2/2 + 30*o - 544. Determine a, given that y(a) = 0.
-1, 6/11
Let i = 667/1995 - 9/133. Let i - 2/15*y**2 - 2/15*y = 0. Calculate y.
-2, 1
Let h(l) be the first derivative of 2*l**5/5 - 5*l**4/2 + 14*l**3/3 - 3*l**2 + 97. Determine r so that h(r) = 0.
0, 1, 3
Let k(l) = l**3 + l**2 - 2*l + 4. Let n(i) = -2*i + 20. Let w be n(10). Let m be k(w). What is r in -2/3*r**m - 1/2*r**5 + 13/6*r**3 + 4/3 + r**2 - 10/3*r = 0?
-2, 2/3, 1
Let g be 92 - 87 - ((-30)/(-8) + 1). Find j, given that -1/4*j + 1/4 - 1/4*j**2 + g*j**3 = 0.
-1, 1
Factor -9*a + 7 + 8 - 39 + 12 - 17*a - 2*a**3 - 16*a**2.
-2*(a + 1)**2*(a + 6)
Let u be (6/2 - 7)/1. Let p = -1 - u. Factor 3*f**2 + f**2 - f**3 + 1 - 5*f**2 + 4*f**2 - p*f.
-(f - 1)**3
Let b(d) be the third derivative of -49*d**6/40 - 11*d**5/4 - 3*d**4/4 + 128*d**2. Factor b(k).
-3*k*(k + 1)*(49*k + 6)
Let h(g) = 2*g**3 - 27*g**2 + 99*g + 131. Let x(z) = 6*z**3 - 82*z**2 + 296*z + 392. Let m(c) = 8*h(c) - 3*x(c). Let m(u) = 0. What is u?
-1, 8
Let -28*c**4 - 16*c + 12*c**2 + 16*c**3 - 16 + c**4 + 31*c**4 = 0. What is c?
-2, -1, 1
Let a be 31*(7 - 1070/155). Solve -8/3*r**2 + 16/3*r + 1/3*r**a + 0 = 0.
0, 4
Let l(r) = r**3 - 3*r + 2. Let n be l(2). Suppose -o + 7 = 3*s - 1, n*s = 8. Factor 3*u**3 + 7 - u - 2*u**o - 2*u - 5.
(u - 1)*(u + 1)*(3*u - 2)
Let m(s) be the first derivative of s**6/144 - s**5/16 + 5*s**4/24 - 3*s**3 - 4. Let w(p) be the third derivative of m(p). Factor w(y).
5*(y - 2)*(y - 1)/2
Let s(v) be the first derivative of 3 - 5/7*v**2 + 8/21*v**3 - 1/14*v**4 + 4/7*v. Factor s(m).
-2*(m - 2)*(m - 1)**2/7
Let z(b) be the first derivative of 18*b**5 + 6*b + 40*b**3 - 45/2*b**2 - 75/2*b**4 - 7/2*b**6 + 1. Factor z(p).
-3*(p - 1)**4*(7*p - 2)
Solve -4/7*h**4 - 376/7*h**2 - 64/7*h**3 - 960/7*h - 900/7 = 0 for h.
-5, -3
Let y = -8561 + 17125/2. Factor -7/6 + 5/2*d + 1/6*d**3 - y*d**2.
(d - 7)*(d - 1)**2/6
Let i(o) be the first derivative of -1/7*o**3 + 0*o - 10 - 3/28*o**4 + 3/7*o**2. Factor i(l).
-3*l*(l - 1)*(l + 2)/7
Suppose -4*c + 2*d + 12 = -4, 2*c = 2*d + 12. Let s = 0 + c. Find j, given that -6*j + 2*j + 2*j - 15*j**s - 7*j = 0.
-3/5, 0
Factor -1/4*y + 0 - 1/2*y**2 + 0*y**3 + 1/4*y**5 + 1/2*y**4.
y*(y - 1)*(y + 1)**3/4
Let f(p) be the second derivative of p**6/72 + p**5/6 + 5*p**4/8 - 17*p**3/3 + 14*p. Let b(i) be the second derivative of f(i). Factor b(v).
5*(v + 1)*(v + 3)
Let m(i) be the first derivative of -i**4/4 + 10*i**3/3 - 25*i**2/2 - 200. Suppose m(o) = 0. What is o?
0, 5
Find o, given that 35*o + 15*o**2 - 4*o**4 + o**4 + 470*o**3 - 505*o**3 - 12 = 0.
-12, -1, 1/3, 1
Suppose 170 - 339 + 178 = 3*l. Find s, given that 4/3 - 4/3*s - 8/3*s**2 + 8/3*s**l - 4/3*s**5 + 4/3*s**4 = 0.
-1, 1
Suppose l + 162 = -4*n - l, 2*n = 3*l - 61. Let a = n + 100. Factor 90*z**4 - 5*z**5 + 46*z**3 + 21*z**5 + 24*z**2 + 5*z**5 + a*z**3.
3*z**2*(z + 2)**2*(7*z + 2)
Let m be 3 + -3 - (-1954)/26. Let s = -75 + m. Factor 0*l**2 + 0 + 2/13*l - s*l**3.
-2*l*(l - 1)*(l + 1)/13
Suppose 5*b + 2 = 17. Let h = -30 + 33. Factor 4*k**b + k**3 - 4*k**h - 2*k**3.
-k**3
Let z = 14258 + -28515/2. Suppose 0 - 1/2*j**4 + z*j**5 - 3/2*j**3 + j + 1/2*j**2 = 0. What is j?
-1, 0, 1, 2
Let y(s) = 3*s**3 - 6*s**2 - 30*s + 3. Let g(o) = 2*o**2 + o - 1. Let b(h) = 3*g(h) + y(h). Factor b(a).
3*a*(a - 3)*(a + 3)
Let r be 128/14 - 1*9. Let b(j) be the third derivative of 0*j + 1/21*j**4 - 5*j**2 - 1/210*j**5 - r*j**3 + 0. Determine s so that b(s) = 0.
1, 3
Suppose 2*t = 2*g - 138, -g + 310 = -5*t - 3*g. Let u be 3/4*t/(-12). Factor 1/2*q**5 + 2/3*q**3 - 4/3*q**u + 1/3 + q**2 - 7/6*q.
(q - 1)**3*(q + 1)*(3*q - 2)/6
Let q(a) be the first derivative of -3*a**5/25 - 3*a**4/20 + 16*a**3/5 - 6*a**2 + 117. Let q(h) = 0. What is h?
-5, 0, 2
Suppose 77 = -4*c + 101. Let z(p) be the third derivative of 0 + 0*p + 1/80*p**5 - 1/96*p**4 - 1/160*p**6 + 0*p**3 - c*p**2 + 1/840*p**7. Factor z(t).
t*(t - 1)**3/4
Let x be 1 - (-11)/(-9) - (-13)/45. Let j(g) be the third derivative of 0*g + 0 - 2*g**3 - x*g**5 - 8*g**2 - 2/3*g**4. Factor j(a).
-4*(a + 1)*(a + 3)
Solve -2/9*p**4 + 2/9*p**2 + 4/9*p + 2/9*p**5 + 0 - 2/3*p**3 = 0.
-1, 0, 1, 2
Suppose 2*f + 0*f + 3*h - 23 = 0, -4*f + 21 = h. Let b be 3 - (-184)/(-96) - 1/f. What is r in -1/6*r**3 + b*r**2 - 4/3*r + 2/3 = 0?
1, 2
Let v = 37 + -60. Let j = 25 + v. Factor -u**j + 7*u + u**3 - 7*u.
u**2*(u - 1)
Let w(k) = -15*k**3 + k**2 - k + 1. Let j be w(1). Let m be (-3 - 1) + (-84)/j. Factor -5*l - 3*l**m - l + 3*l**2 - 3*l**2.
-3*l*(l + 2)
Let a = 53 - 50. Factor -7*v**5 + 9*v**a - 7*v**2 + 8*v**5 + 11*v**4 - 16*v**4 + 2*v.
v*(v - 2)*(v - 1)**3
Find y such that 0 + 27/4*y - 3/4*y**3 + 3/4*y**4 - 27/4*y**2 = 0.
-3, 0, 1, 3
Let a(b) be the first derivative of -2*b**7/21 - 8*b**6/45 + 4*b**5/15 - 3*b - 17. Let h(s) be the first derivative of a(s). Factor h(m).
-4*m**3*(m + 2)*(3*m - 2)/3
Let y(a) = 5*a**2 + 12*a. Let q(i) = -11*i**2 - 24*i. Let j be (-3 - 2)/(-1 + 2). Let s(m) = j*y(m) - 2*q(m). Factor s(b).
-3*b*(b + 4)
Let b(s) be the second derivative of 3*s + 0 + 1/900*s**6 - 1/30*s**4 - 1/300*s**5 + 0*s**2 - 1/3*s**3. Let z(x) be the second derivative of b(x). Factor z(w).
2*(w - 2)*(w + 1)/5
Let g(r) = -r**2 + 10*r + 34. Let b(v) = 4*v**2 - 38*v - 137. Let s(o) = 4*b(o) + 18*g(o). Let s(c) = 0. What is c?
-2, 16
Let j(l) be the third derivative of -l**6/180 - l**5/30 + 4*l**3/9 + 72*l**2 + 3*l. Factor j(q).
-2*(q - 1)*(q + 2)**2/3
Factor 1/7*x**4 + 0*x + 10/7*x**3 + 0 + 9/7*x**2.
x**2*(x + 1)*(x + 9)/7
Let b(v) be the second derivative of v**5/5 - 11*v**4/3 + 26*v**3 - 90*v**2 - 79*v + 2. Factor b(g).
4*(g - 5)*(g - 3)**2
Let s(r) be the first derivative of r**7/4200 + r**6/600 + r**5/200 + r**4/120 - 17*r**3/3 + 3. Let d(w) be the third derivative of s(w). Solve d(m) = 0.
-1
Let k = -76 + 78. Suppose 2*z = -3*d + k*d, -2*d = 0. Factor 2/3*n**2 - 2/9*n + z + 8/9*n**3.
2*n*(n + 1)*(4*n - 1)/9
Let y(j) = -4*j**3 + 266*j**2 + 135*j - 62. Let h be y(67). Find n, given that 0 + 0*n**2 - 1/8*n**3 - 1/8*n**h - 1/4*n**4 + 0*n = 0.
-1, 0
Find f such that -34/3*f - 6 + 2/3*f**3 - 14/3*f**2 = 0.
-1, 9
Factor -24 - 24*q - 39*q**2 + 7*q**2 + 56*q**3 - 28*q - 60*q**3.
-4*(q + 1)**2*(q + 6)
Let d be (9/(-6) + 1)*0. Suppose d = -3*g + 4*i, g + 1 = i + 2. Factor 3*j**g - 5*j**4 + j**3 - 3*j**3.
-2*j**3*(j + 1)
Let o(q) be the third derivative of 0*q**3 + 3/665*q**7 + 0*q**4 - 1/57*q**6 + 0*q + 0 + 10*q**2 + 2/285*q**5. Factor o(l).
2*l**2*(l - 2)*(9*l - 2)/19
Factor -8*u**3 - 3*u**4 + 0*u**5 - 2*u**4 - u**5 + 36*u**2 - 40*u**2.
-u**2*(u + 1)*(u + 2)**2
Let c(w) be the third derivative of w**6/60 + w**5/10 - w**4/3 + 127*w**2. Factor c(q).
2*q*(q - 1)*(q + 4)
Solve 2/11*n**5 - 14/11*n**4 + 0 - 34/11*n**2 + 34/11*n**3 + 12/11*n = 0 for n.
0, 1, 2, 3
Let s(n) = -8*n**3 + 28*n**2 + 64*n + 64. Let m(v) = v**3 - v**2 - v - 1. Let c(d) = -10*m(d) - s(d). Determine w, given that c(w) = 0.
-3
Let g be ((-198)/30 + 7)/(-4 - -5). Factor -2/5*l**2 - g*l + 4/5.
-2*(l - 1)*(l + 2)/5
Suppose 22*n - 12 - 6 = 26. Factor -3/8*t**4 + 45/2*t - 69/4*t**n - 75/8 + 9/2*t**3.
-3*(t - 5)**2*(t - 1)**2/8
Let 0 + 9/4*c**4 + 1/2*c**5 + 3*c**3 + 0*c + c**2 = 0. Calculate c.
-2, -1/2, 0
Suppose -5*l - 1 = z - 3*z, 5*l + z - 8 = 0. Let d be 4*(-7)/(-24) - l. Factor 1/6*i**3 + 1/3*i**2 + d*i + 0.
i*(i + 1)**2/6
Suppose -4 = 50*g - 51*g. Let q(v) be the second derivative of 1/2*v**g + 0 + 1/10*v**5 + v**2 + v**3 - 5*v. Let q(y) = 0. What is y?
-1
Let l be ((-6)/9)/(1/(-33)). Factor l + 3*h**2 + 51 + 81*h + 3*h**3 + 8 + 24*h**2.
3*(h + 3)**3
Suppose 0 = 5*h - 3 - 7. Suppose h = 4*c - 6. Factor -x**c + 6*x**2 - 2