, 0
Let 1/7*x**3 - 6/7 - 1/7*x + 6/7*x**2 = 0. Calculate x.
-6, -1, 1
Let w(k) be the first derivative of 5*k**3/3 + 895*k**2 + 160205*k + 279. Determine x so that w(x) = 0.
-179
Let l(v) be the second derivative of -v**4/78 - 44*v**3/39 - 484*v**2/13 - v - 30. Factor l(u).
-2*(u + 22)**2/13
Let n(l) be the second derivative of -l**5/70 + l**3/21 + l - 17. Factor n(o).
-2*o*(o - 1)*(o + 1)/7
Let r(c) = 3*c + 38. Let b be r(-12). Let u(x) be the second derivative of 3/2*x**b + 1/4*x**4 + x**3 + 0 - 4*x. Find f, given that u(f) = 0.
-1
Let s(i) be the first derivative of 2/5*i**5 + 0*i - 2*i**4 + 10/3*i**3 + 18 - 2*i**2. Factor s(z).
2*z*(z - 2)*(z - 1)**2
Suppose 4/5*w - 4/5*w**2 + 4/5*w**4 + 0 - 4/5*w**3 = 0. What is w?
-1, 0, 1
Let w(f) be the second derivative of -f**4/12 - f**3 - 3*f**2/2 + 3*f. Let a be w(-5). Factor -2*s**2 - 5*s - a - 3*s + 0 - 4*s**2.
-2*(s + 1)*(3*s + 1)
What is l in 42 - 3*l**2 + 2*l**2 + 21 - 60*l + 6*l**2 - 8*l**2 = 0?
-21, 1
Find f such that 1/2*f**4 - 3*f - 1/2*f**2 + 3*f**3 + 0 = 0.
-6, -1, 0, 1
Find p such that -24/13*p + 0 - 2/13*p**3 + 16/13*p**2 = 0.
0, 2, 6
Find t, given that 67/3*t**2 + 1 + 53/6*t - 20/3*t**4 - 8/3*t**5 + 21/2*t**3 = 0.
-3, -1, -1/4, 2
Let g(j) = -20*j**2 - 168*j - 84. Let q(f) = f**2 - 2*f + 3. Let i(l) = g(l) + 8*q(l). Determine m, given that i(m) = 0.
-15, -1/3
Suppose 34*r - 35*r = -1. Let m be (-10)/(-45) + (r - (-2685)/189). Factor 81/7*v**3 - 162/7*v**2 - 24/7 + m*v.
3*(3*v - 2)**3/7
Factor 69*w**3 - 21*w**3 + 117*w**3 - 4*w**4 + 475*w - 624*w**2 - 204 + 141*w + 51*w**3.
-4*(w - 51)*(w - 1)**3
Suppose -h = -4*p, 0 = 3*h - h - 8. Let z be 3 + 0 + p + 5. Factor -29 + 63 + z*m + 3*m**2 - 28.
3*(m + 1)*(m + 2)
Suppose -2*m = -3*t - 2, 5*t + 2*m - 6 = 3*m. Let g = 218 + -215. Factor 1/4*w**g + 1/4*w**t - 1/4*w - 1/4*w**4 + 0.
-w*(w - 1)**2*(w + 1)/4
Find h, given that 54*h**3 - 44*h**4 + h + 10*h + 1 + 17*h**4 + 6*h**2 + 36*h**2 - 81*h**5 = 0.
-1/3, 1
Let u(y) = y**3 - 33*y**2 - 30*y - 134. Let q be u(34). Solve -10*j - 35/4*j**q - 5/4*j**3 + 20 = 0.
-4, 1
Let k(i) be the second derivative of -i**4/138 + 29*i**3/69 - 54*i**2/23 - 23*i. Factor k(j).
-2*(j - 27)*(j - 2)/23
Let t = 63 + -59. Factor -3*k**5 - k - k**2 - 6*k**2 + 6*k**t + 4*k + k**2.
-3*k*(k - 1)**3*(k + 1)
Factor -20/9*c + 0 + 2/9*c**2.
2*c*(c - 10)/9
Let m be (2/8)/((-4)/(-32)*6). Let n = 68/3 + -20. Suppose -n*o + m*o**2 + 7/3*o**3 - 5/3*o**4 + 1/3*o**5 + 4/3 = 0. Calculate o.
-1, 1, 2
Let l = 986 - 986. Let r(i) be the first derivative of l*i**2 + 8 + 0*i + i**4 - 8/3*i**3 + 4/5*i**5. Solve r(y) = 0.
-2, 0, 1
Suppose -2*t + 10 = 3*n, t - 6 = 85*n - 87*n. Factor 8/3 + 4*b - 8/3*b**n.
-4*(b - 2)*(2*b + 1)/3
Let r(y) be the third derivative of 0*y + 0*y**3 + 0 - 7/150*y**5 + 1/840*y**8 + 3/100*y**6 - 9*y**2 - 1/105*y**7 + 1/30*y**4. Factor r(i).
2*i*(i - 2)*(i - 1)**3/5
Suppose 2*x + 12 = 3*k, -2*k = -2*x + 3 - 11. Suppose 4*w + 5*m = 43, w - k*m = 5*w - 40. Factor w*j + 11*j - 6 - 5*j - 12*j**2 + 2*j + 3*j**3.
3*(j - 2)*(j - 1)**2
Let s(f) = -13*f - 26. Let c be s(12). Let q = c - -414. Let -q*w**4 + 9*w**3 + w**3 + 207*w**4 - 35*w**5 = 0. What is w?
-1, 0, 2/7
Let v(q) be the first derivative of -q**4/16 - 4*q**3 - 96*q**2 - 5*q - 50. Let o(m) be the first derivative of v(m). Solve o(a) = 0.
-16
Let n(s) = 2*s**4 + 14*s**3 + 128*s**2 + 204*s + 108. Let c(w) = w**4 - w**3 + w**2 - 3*w - 1. Let m(i) = -4*c(i) + n(i). What is y in m(y) = 0?
-2, -1, 14
Solve -8*p + 6/7*p**3 - 24/7 - 34/7*p**2 + 2/7*p**5 + 10/7*p**4 = 0.
-3, -2, -1, 2
Let r = -5 + 5. Suppose r*t - 8 = -2*t. Solve 0*z - t*z + 0*z - 3*z**2 - 5*z = 0.
-3, 0
Let z be 1 - 12/(6 - 12). Let s(v) be the first derivative of -5 + 4*v + 0*v**3 - 1/2*v**4 + z*v**2. Factor s(h).
-2*(h - 2)*(h + 1)**2
Suppose -13 + 7 = -6*u. Factor -h**3 - u + 4 - 5 + 3*h.
-(h - 1)**2*(h + 2)
Let a = -409 + 289. Let h be (a/63)/(-4)*6/5. Factor -18/7*m**2 + h*m + 0.
-2*m*(9*m - 2)/7
Let i(p) be the second derivative of -p**7/126 - p**6/18 - p**5/10 + p**4/9 + 4*p**3/9 + 8*p + 1. What is w in i(w) = 0?
-2, 0, 1
Let n(x) = 20*x**3 - 6*x**2 + 18*x + 18. Let y(q) = q**2 + q - 10. Let w be y(3). Let b(h) = h**3 + h + 1. Let g(z) = w*n(z) - 36*b(z). Let g(r) = 0. What is r?
0, 3
Let c(q) be the second derivative of 1/2*q**3 + 1/10*q**6 + 30*q + 0 - 1/2*q**4 + 1/14*q**7 + 3/2*q**2 - 3/10*q**5. Suppose c(h) = 0. What is h?
-1, 1
Suppose 0*u + 2/3*u**2 + 0 - 4/9*u**3 - 2/9*u**4 = 0. What is u?
-3, 0, 1
Let p = 115 - 102. Let h(z) = z**2 - 9*z - 52. Let o be h(p). Factor i**2 - i**4 + 0 + o*i + 1/2*i**5 - 1/2*i**3.
i**2*(i - 2)*(i - 1)*(i + 1)/2
Let z(l) be the third derivative of l**8/84 - 52*l**7/735 - 5*l**6/21 + 16*l**5/7 - 39*l**4/14 - 36*l**3/7 - 53*l**2. Let z(h) = 0. What is h?
-3, -2/7, 1, 3
Let r(u) be the first derivative of -45/16*u**4 - 1/2*u + 10 - 4*u**3 - 17/8*u**2. Suppose r(d) = 0. What is d?
-2/5, -1/3
Let a(h) be the first derivative of -h**5/12 + 15*h**4/4 - 135*h**3/2 + 5*h**2 + 30. Let o(s) be the second derivative of a(s). Factor o(g).
-5*(g - 9)**2
Let c(m) be the first derivative of -15/8*m**2 + 3/2*m + 3/16*m**4 + 3/4*m**3 - 18 - 3/20*m**5. Factor c(v).
-3*(v - 1)**3*(v + 2)/4
Let p = 35 + -31. Factor 32*b**3 + 19*b**2 - 4 + 5*b**2 + b**p + 5*b**4 + 6*b**4.
4*(b + 1)**3*(3*b - 1)
Let q = 15 + 17. Let w be 3 + -22*4/q. Factor 3/4*y**2 + 0 - 3/4*y**4 + 1/4*y**3 - w*y.
-y*(y - 1)*(y + 1)*(3*y - 1)/4
Let w = 74722/11 - 6790. Let 18/11*z + w*z**2 + 28/11*z**3 + 4/11 + 12/11*z**4 + 2/11*z**5 = 0. What is z?
-2, -1
Let g be 3/(-9)*3 - -4. Let -12*y**g - 44*y**2 - 102 - 48*y + 0*y**3 + 86 = 0. What is y?
-2, -1, -2/3
Let h(d) be the first derivative of -d**3/30 - 12*d**2 - 1440*d - 556. Find j such that h(j) = 0.
-120
Suppose 28*k**2 + 16/3*k**3 + 6*k - 2/3*k**5 - 36 - 8/3*k**4 = 0. Calculate k.
-3, -2, 1, 3
Let k = 28 - 26. Factor 4 + 2*p**2 - p**2 - 2*p**k + 2*p - p**2.
-2*(p - 2)*(p + 1)
Factor 0*w - 1/2*w**2 + 1/2.
-(w - 1)*(w + 1)/2
What is n in 12*n - 13/3*n**3 + n**4 - 7/3*n**2 + 1/3*n**5 - 20/3 = 0?
-5, -2, 1, 2
Let i(s) be the second derivative of s**5/10 + 13*s**4/30 - 2*s**3/5 + 290*s. Suppose i(k) = 0. What is k?
-3, 0, 2/5
Let l(c) be the second derivative of 0 + 0*c**2 + 3/50*c**6 + 1/20*c**4 + 1/70*c**7 + 9/100*c**5 + 0*c**3 + 6*c. Factor l(d).
3*d**2*(d + 1)**3/5
Suppose 3 = l - 0*l. Let q = -65 + 67. Suppose -29*r + r**l + 2*r**q + 29*r = 0. Calculate r.
-2, 0
Let z be 849/18 - 1/6. Factor 4*w**2 - w**3 + z*w - w**3 - 49*w.
-2*w*(w - 1)**2
Let g(u) be the second derivative of -u**4/20 - 13*u**3/10 + 21*u**2/5 - 279*u. Factor g(y).
-3*(y - 1)*(y + 14)/5
Let -3/7*h - 6 + 6*h**2 + 3/7*h**3 = 0. Calculate h.
-14, -1, 1
Let l(q) = -100*q**2 - 2105*q - 675. Let z(b) = 11*b**2 + 234*b + 75. Let r(i) = 4*l(i) + 35*z(i). Factor r(k).
-5*(k + 15)*(3*k + 1)
Let c be 46/3 - 5/15. Let u(y) = -y**3 - 6*y**2 - 5*y - 2. Let d(x) = -6*x**3 - 42*x**2 - 36*x - 15. Let f(j) = c*u(j) - 2*d(j). Let f(n) = 0. Calculate n.
-1, 0
Factor -15/2*s + 3/4*s**2 - 33/4.
3*(s - 11)*(s + 1)/4
Let g(p) be the second derivative of p**6/450 + p**5/50 + p**4/15 + 4*p**3/3 - 17*p. Let x(s) be the second derivative of g(s). Factor x(b).
4*(b + 1)*(b + 2)/5
Let t be ((-2)/80*-6)/(117/318). Let l = t - 1/130. Factor 0 + l*m**2 + 0*m.
2*m**2/5
Let m(o) be the second derivative of 0 + 0*o**3 - 4*o**2 - 1/21*o**7 + 11*o + 7/6*o**4 + 1/10*o**5 - 1/5*o**6. Suppose m(i) = 0. What is i?
-2, -1, 1
Let r(o) = 2*o**2 - 3*o + 4. Let m(h) be the first derivative of h**3/3 - h**2/2 + 26. Let l(g) = 3*m(g) - r(g). Find k, given that l(k) = 0.
-2, 2
Suppose -3/2*l**3 + 0 + 9/2*l - 3*l**2 = 0. Calculate l.
-3, 0, 1
Let y = -1918 + 21108/11. Factor -8/11 - 2/11*v**2 - y*v.
-2*(v + 1)*(v + 4)/11
Suppose 1853*q**3 + 111*q**3 - 410*q**2 + 2033*q**2 + 1077*q**4 + 21*q**5 + 237*q**3 + 294*q + 184*q**3 = 0. What is q?
-49, -1, -2/7, 0
Suppose 0 = 4*o - 0*o - 16, -4*o = -4*m + 4. Solve u**5 - m*u**4 + 6*u**4 - u**3 - u**2 + 0*u**4 = 0 for u.
-1, 0, 1
Let i(h) = -h**2 - 12*h - 33. Let a be i(-5). Factor 14/5*q**a - 32/5*q + 8/5.
2*(q - 2)*(7*q - 2)/5
Let a(o) = -o + 3. Suppose p = -4*p. Let d be a(p). Factor -7/4*n + 7/4*n**d - 3/4*n**2 - 1/2 + 5/4*n**4.
(n - 1)*(n + 1)**2*(5*n + 2)/4
Suppose 9 = -4*o - 0*o + 3*a, -3*a + 9 = 4*