20 + k**4/4 - 8*k**2. Let f(t) be the second derivative of n(t). Factor f(j).
3*(j - 1)**2/8
Let t(b) be the first derivative of b**8/2184 + b**7/1365 - b**6/780 - b**5/390 - 6*b**2 + 11. Let g(l) be the second derivative of t(l). What is a in g(a) = 0?
-1, 0, 1
Factor 25*r**3 - 60*r**2 - 3*r**4 + 45*r**3 + 65 - 4*r**4 - 2*r**4 - 70*r + 4*r**4.
-5*(r - 13)*(r - 1)**2*(r + 1)
Let b(n) = -n**3 + 3*n**2 - n + 8. Let j be b(4). Let z be (2 + 0)*(-30)/j. Let 18*d**2 + 0*d**4 - 18*d**3 - 3*d - 2*d**4 - 2*d + 6*d**z + d = 0. Calculate d.
-2, 0, 1/3, 1
Let s(c) be the third derivative of 0*c**4 + 3*c**2 - 1/105*c**7 + 1/30*c**6 + 0*c + 0*c**3 + 1/10*c**5 + 0. Factor s(z).
-2*z**2*(z - 3)*(z + 1)
Let t = -5452/63 + 784/9. Find y, given that -24/7*y**2 + t*y**5 + 0 + 4*y**3 - 32/7*y + 24/7*y**4 = 0.
-4, -2, -1, 0, 1
Suppose -n - 21 = -5*q, -4*n = 3*q - 4 - 4. Let k be 0 + (-1)/(-2)*q. Factor -10*z**5 - z**k + z**2 + 2*z**4 + 9*z**5.
-z**4*(z - 2)
Let c(h) be the first derivative of -28*h**3/3 - 32*h**2 - 16*h - 66. Factor c(r).
-4*(r + 2)*(7*r + 2)
Let l(t) be the third derivative of -t**7/252 + 17*t**6/720 - t**5/360 - 17*t**4/144 + t**3/6 + 10*t**2 + 3*t. Determine w so that l(w) = 0.
-1, 2/5, 1, 3
Let f = -102 - -129. Let 3*w**3 - 2*w**3 + 9*w + f*w**2 + 20*w**2 - 53*w**2 = 0. Calculate w.
0, 3
Let z(b) = b**3 - 15*b**2 + 4*b + 142. Let u be z(14). Factor -8/3*a**u + 0 + 4/3*a.
-4*a*(2*a - 1)/3
Let b(u) be the third derivative of 3/40*u**6 + 0*u**3 - 26*u**2 + 0 - 1/8*u**4 + 0*u + 1/10*u**5. Factor b(z).
3*z*(z + 1)*(3*z - 1)
Let j = 45 + -43. Factor 3*q**5 - 2*q**5 - 23*q**3 + 3*q**j + q**4 - 4*q**2 + 22*q**3.
q**2*(q - 1)*(q + 1)**2
Let j be 1*(-22 - -4) + -2. Let u be (4 - 1) + 52/j. What is z in -1/5 + u*z - 1/5*z**2 = 0?
1
Find d, given that 2/3*d**2 + 0 - 4/3*d = 0.
0, 2
Let g(u) be the first derivative of u**6/7 + 6*u**5/5 + 27*u**4/7 + 44*u**3/7 + 39*u**2/7 + 18*u/7 - 437. Find h, given that g(h) = 0.
-3, -1
Let r(b) be the first derivative of 0*b - b**4 + 28/5*b**5 + 0*b**2 + 0*b**3 - 4*b**6 + 11. Factor r(o).
-4*o**3*(o - 1)*(6*o - 1)
Suppose 0*m = -5*m + 5*x - 20, 5*x = -m + 32. Let 5/6*g**3 + 1/6*g**4 + 0 + 1/2*g + 7/6*g**m = 0. What is g?
-3, -1, 0
Solve -20 - 35*u - 55 - 35*u**2 - 16*u + 38*u**2 + 21 = 0.
-1, 18
Let l(p) be the second derivative of -p**4/12 - 14*p**3/3 + 29*p**2/2 + 11*p + 1. Solve l(z) = 0.
-29, 1
Let r(x) be the second derivative of -x**4/3 + 20*x**3 + 128*x**2 + 2*x - 71. Solve r(l) = 0 for l.
-2, 32
Determine d, given that -d - d**2 + 189 - 187 + 0*d = 0.
-2, 1
Let t be 1*-2*20/(-10). Determine f so that 64*f + 5*f**4 + 96*f**3 - 5*f**4 - 20*f**4 + 4*f**5 - 12*f**t - 128*f**2 = 0.
0, 2
Let b(s) be the first derivative of -s**3/12 + s**2/8 + 75. Factor b(q).
-q*(q - 1)/4
Let n(l) be the first derivative of -13*l**3/3 + 45*l**2/2 - 33*l + 26. Let p(v) = -27*v**2 + 91*v - 67. Let j(c) = 5*n(c) - 3*p(c). Find y such that j(y) = 0.
3/2
Let r(o) = 20*o**3 - 120*o**2 + 89*o - 21. Let t(w) = -w**3 + w - 1. Let i(f) = 3*r(f) - 15*t(f). Suppose i(z) = 0. Calculate z.
2/5, 4
Let s = -44/217 + 1786/2387. What is r in 24/11*r**4 + 8/11*r**3 + s*r - 28/11*r**2 + 4/11 - 14/11*r**5 = 0?
-1, -2/7, 1
Let j(k) be the first derivative of -k**7/1365 + k**6/390 - 23*k**2/2 - 6. Let x(n) be the second derivative of j(n). Factor x(v).
-2*v**3*(v - 2)/13
Let s(l) = -l**2 - 6*l - 1. Let w be s(-5). Factor 4 - o**3 - w + 333*o**2 - 2*o - 336*o**2.
-o*(o + 1)*(o + 2)
Let p(y) be the first derivative of 28*y**3/9 - 2*y**2/3 - 32*y/3 + 306. What is m in p(m) = 0?
-1, 8/7
Suppose -48/11 - 91/11*v**2 + 194/11*v = 0. Calculate v.
2/7, 24/13
Suppose 32/15 - 36/5*g + 22/5*g**2 + 2/3*g**3 = 0. Calculate g.
-8, 2/5, 1
Let p be 2/(-3 - -1) - (-8 - 5). Let r be (-134)/(-88) - p/48. Factor r*i**2 - 8/11 + 10/11*i**3 - 16/11*i.
2*(i - 1)*(i + 2)*(5*i + 2)/11
Suppose -5*i - 20 = 5*p, 3*p - 5*i = p - 22. Let k be (-4)/(-8) + (-1)/p. Find l such that 0 + 2/3*l + k*l**2 = 0.
-1, 0
Let i = 13815 + -13810. Suppose l + 2*l = 4*f + 18, -2*f - 2 = 2*l. What is r in 0*r + 0 + 2/9*r**2 + 2/3*r**4 + l*r**i - 10/9*r**3 = 0?
-1, 0, 1/3
Let p(r) be the second derivative of -r**4/12 + 17*r**3/6 + 42*r**2 + 477*r. Find u, given that p(u) = 0.
-4, 21
Let p = 1588 - 1581. Let x(v) be the second derivative of -1/147*v**p - 4*v + 0 - 1/105*v**6 + 1/42*v**4 + 0*v**2 + 0*v**3 + 1/70*v**5. Solve x(a) = 0 for a.
-1, 0, 1
Suppose -12 = -2*d - 4. Suppose x = 3*p - 10, 14*p - 15*p - 15 = -d*x. Find r, given that 0*r**4 + 0*r**2 + 1/5*r + 0 - 2/5*r**3 + 1/5*r**p = 0.
-1, 0, 1
Let g(y) = -2*y - 4. Let d(o) = -4*o - 8. Let m(f) = -6*d(f) + 11*g(f). Let p be m(8). Factor -4*k**2 - k - 11*k**3 - 14*k**4 + p*k**4 + 10*k**2.
k*(k - 1)*(2*k - 1)*(3*k - 1)
Let j = 1947/5 + -388. Let t(q) be the first derivative of 3/2*q**6 + 0*q - 5 + q**2 - 11/4*q**4 + 7/3*q**3 - j*q**5. Let t(n) = 0. What is n?
-1, -2/9, 0, 1
Let h(v) = -v**3 + 124*v**2 - 595*v + 2. Let u be h(119). Let f = 448/5 + -89. Factor -2/5*m**u - f*m + 2/5.
-(m + 2)*(2*m - 1)/5
Suppose 5 = -3*u + 26. Suppose 5*b + 5*p - 13 = u, -16 = 5*b - 4*p. Factor r**2 + 2 + 3*r**2 + b*r**2 + 4*r - 2*r**2.
2*(r + 1)**2
Factor 6/7*q**2 - 8/7 + 10/7*q + 2/7*q**4 - 10/7*q**3.
2*(q - 4)*(q - 1)**2*(q + 1)/7
Let x(s) = s**3 + 3*s**2 - s - 1. Let b be x(-3). Factor j**4 + 21*j**2 + b + 123*j**3 + 3*j**4 + 18*j - 107*j**3 - 7*j.
(j + 1)*(j + 2)*(2*j + 1)**2
Let g = 638 - 635. Let p(z) be the second derivative of 1/6*z**4 - 2/3*z**g - 9*z + z**2 + 0. Factor p(v).
2*(v - 1)**2
Let v(s) = s**3 + s**2 - 1. Let i(f) = 7*f**3 - 69*f**2 - 2*f + 69. Let c(x) = -i(x) + 5*v(x). Let c(q) = 0. What is q?
-1, 1, 37
Let q(c) be the second derivative of 3/4*c**3 - 1/4*c**4 + 0 - 15*c - 3/40*c**5 + 0*c**2. Suppose q(y) = 0. What is y?
-3, 0, 1
Let t(p) be the third derivative of -p**7/3360 - p**6/720 + p**5/160 - 25*p**3/6 - 24*p**2. Let h(d) be the first derivative of t(d). Factor h(w).
-w*(w - 1)*(w + 3)/4
Let a = 17/15 + -4/5. Let r be 7 + -3 - 5 - -3. Let 0 - a*s**r + 0*s = 0. What is s?
0
Let t(j) be the third derivative of j**7/210 + j**6/15 + j**5/12 - 25*j**4/12 - 5*j**2 - 17. Factor t(y).
y*(y - 2)*(y + 5)**2
Let s = -13888/5 - -2778. Let s*f**3 + 24/5*f**2 + 4/5 - 8/5*f**4 - 22/5*f = 0. Calculate f.
-2, 1/4, 1
Factor -56*m**2 - 125 - 135*m - 5*m**3 - 52*m - 79*m**2 + 10*m - 78*m.
-5*(m + 1)**2*(m + 25)
Factor -12 - 12*j**2 - 2*j**3 - 44*j + 13*j + 9*j.
-2*(j + 1)*(j + 2)*(j + 3)
Let p = -22047 + 22049. Factor -1/3*i**p - 8/3 + 3*i.
-(i - 8)*(i - 1)/3
Let t = 2/105 + 101/210. Let c(n) be the first derivative of t*n**6 - n**3 - 9/4*n**4 + 0*n + 6 + 3*n**2 + 3/5*n**5. What is w in c(w) = 0?
-2, -1, 0, 1
Let o = -82012/11 - -7456. Find y, given that 0*y + 2/11*y**2 + 2/11*y**4 + 0 - o*y**3 = 0.
0, 1
Let i(k) = 2*k**4 + 9*k**3 - 12*k**2 - 25*k. Let o(r) = -r**4 - 9*r**3 + 13*r**2 + 25*r. Let g(t) = 2*i(t) + 3*o(t). Factor g(j).
j*(j - 5)**2*(j + 1)
Suppose 0 = 6*t - 16*t. Suppose 0*i + 0*i**3 + t - 2/9*i**4 + 2/9*i**2 = 0. What is i?
-1, 0, 1
Let b be (-4)/6*(2 + -10 - -5). Let z(k) be the second derivative of k - 1/3*k**3 + 1/6*k**4 + 0 + 0*k**b. What is q in z(q) = 0?
0, 1
Let t(w) = -6*w + 184. Let q be (-40)/30*135/(-6). Let k be t(q). Factor 46/3*j + 44/3*j**3 + 25*j**2 + 7/3*j**k + 8/3.
(j + 1)**2*(j + 4)*(7*j + 2)/3
Suppose -4*p - 303 = -5*n, 63 = 6*n - 5*n - 2*p. Let m = 61 - n. Factor 1/5*i**m + 0*i - 1/5.
(i - 1)*(i + 1)/5
Let q(c) be the first derivative of 5 + 2/5*c**2 - 4/15*c**3 + 1/15*c**4 - 5*c. Let f(v) be the first derivative of q(v). Factor f(y).
4*(y - 1)**2/5
Let d = 2405 - 2400. Let x(g) be the second derivative of 0 + 1/12*g**4 - 1/30*g**6 + 0*g**2 + 7*g + 1/20*g**d - 1/6*g**3. Factor x(i).
-i*(i - 1)**2*(i + 1)
Let m be ((-8)/(-28))/((-18)/(-336)). Find c such that 8/3*c**2 - 4*c**3 - 2/3*c**5 + m*c - 10/3*c**4 + 0 = 0.
-2, 0, 1
Find d, given that -5/4*d**3 + 20*d - 20 + 5/4*d**2 = 0.
-4, 1, 4
Suppose 12*o - 72 = -0*o. Suppose -3*f + 3*q = -o, -4*q + 6 + 1 = f. Determine g, given that 0 - 6/7*g**f - 2/7*g - 6/7*g**2 - 2/7*g**4 = 0.
-1, 0
Suppose 24 = -3*t - 126. Let m be 10/t + 13/15. Factor 0 + 2/3*s**3 - m*s**2 + 2/3*s**4 + 0*s - 2/3*s**5.
-2*s**2*(s - 1)**2*(s + 1)/3
Suppose 215 - 224 = -3*y. Factor 0*t**2 - 2/13*t**y + 2/13*t**5 