t h = v + -72. Solve -1/2*c**2 + h*c + 0 + 1/2*c**3 = 0.
0, 1
Let p(u) be the first derivative of u**4/8 + 8*u**3/3 - 9*u**2 + 689. What is l in p(l) = 0?
-18, 0, 2
Let g(t) be the first derivative of 3*t**5/20 + t**4/2 + t**3/4 - t**2/4 - 90. Factor g(n).
n*(n + 1)*(n + 2)*(3*n - 1)/4
Let f(s) be the first derivative of -2*s**3/3 + 5*s + 1. Let p = 77 - 74. Let r(c) = -3*c**2 + c + 6. Let b(a) = p*r(a) - 4*f(a). Factor b(w).
-(w - 2)*(w - 1)
Let t(p) be the second derivative of -18*p - 1/90*p**6 + 0 + 0*p**3 - 1/60*p**5 + 0*p**4 + 0*p**2. Factor t(f).
-f**3*(f + 1)/3
Suppose -f = 5*l - 28, -l + 6 = l + 3*f. Suppose -31 + 1 = -l*i. Factor -18*d - i*d + 7*d - 4*d**2 - 12 + 0*d.
-4*(d + 1)*(d + 3)
Solve 513*f**2 - 729/2 + 243/2*f - 125/2*f**5 - 425/2*f**4 + 5*f**3 = 0.
-9/5, 1
Determine c so that -c**4 + 29*c**2 + 10*c**3 + 0*c**3 + 6*c + 8*c**3 - 16*c**3 + 36*c = 0.
-3, -2, 0, 7
Let t = 2/25647 - -1923517/102588. Let -15/2*s + 3/4*s**2 + t = 0. Calculate s.
5
Suppose -25*u**3 - 27*u**3 + 40*u**2 + 47*u**3 + 50 + 84*u + 11*u = 0. What is u?
-1, 10
Let v(d) = d**2 - 13*d + 7. Let t(s) = 4*s**2 - 2 - 6*s**2 + 12*s - 4. Let z(b) = 2*b - 11. Let c be z(7). Let f(q) = c*t(q) + 2*v(q). Let f(y) = 0. What is y?
1/2, 2
Find o, given that 4/3*o**3 + 104/3*o + 28*o**2 - 8/3*o**4 + 32/3 = 0.
-2, -1, -1/2, 4
Suppose x - 44 = -0*x - 4*c, -5*x = -c - 199. Let j = -38 + x. Suppose u**5 - 32*u + 32*u + j*u**4 = 0. Calculate u.
-2, 0
Suppose b = -5*x - 2*b + 44, 5*x - 5*b = 20. Suppose -x*r + 7 = -7. Factor 1/5*c**5 + 0*c**r + 0*c**4 + 0 - 2/5*c**3 + 1/5*c.
c*(c - 1)**2*(c + 1)**2/5
Solve x**5 - 72*x - 48*x**3 + 34*x - 128*x**2 + 38*x + 0*x**5 = 0 for x.
-4, 0, 8
Let o(q) be the third derivative of -1/570*q**5 + 8*q**2 + 0 - 1/57*q**4 - 1/19*q**3 + 0*q. Solve o(p) = 0 for p.
-3, -1
Let r(o) = -6*o**3 - 4*o**2 - 2*o. Let n(w) = -w**3 - w. Let t = 53 - 52. Let m(c) = t*r(c) - 2*n(c). Factor m(u).
-4*u**2*(u + 1)
Suppose -b = 1 - 3. Factor 2 + k**2 + b + 9*k - 5*k.
(k + 2)**2
Let i(x) be the second derivative of -x**6/12 - 19*x**5/2 - 461*x. Factor i(b).
-5*b**3*(b + 76)/2
Let n(p) be the second derivative of -p**5/4 - 5*p**4/12 + 5*p**3/6 + 5*p**2/2 - 19*p - 2. Determine b, given that n(b) = 0.
-1, 1
Solve 17*s**4 - 4*s - 4*s**3 + 0*s**5 + 5*s**5 - 12*s**2 + 3*s**5 - 5*s**4 = 0.
-1, -1/2, 0, 1
Let d(r) be the second derivative of 5*r**4/12 + 55*r**3/3 + 605*r**2/2 - 15*r. Factor d(h).
5*(h + 11)**2
Let f(u) be the first derivative of u**4/16 + 4*u**3/3 - u**2/8 - 4*u + 213. Determine w so that f(w) = 0.
-16, -1, 1
Let n(i) be the third derivative of 0*i - 1/15*i**5 - 1/60*i**6 + 2/3*i**3 + 0 + 1/12*i**4 - 26*i**2. Factor n(l).
-2*(l - 1)*(l + 1)*(l + 2)
Let w = -1949/15 - -361/3. Let s = -9 - w. Suppose 6/5*u**3 + 9/5*u**2 + 0 - s*u**4 + 0*u = 0. What is u?
-1, 0, 3
Suppose -109 = -4*t + 51. Let d be t/22 + 10/55. What is n in -4*n**3 + d*n**4 + n**5 + 0*n**5 + n**5 + 2*n**3 - 2*n**2 = 0?
-1, 0, 1
Suppose -32*y + 2/7*y**4 - 160/7 - 96/7*y**2 - 8/7*y**3 = 0. What is y?
-2, 10
Let s be ((-15)/270)/((-2)/30). Let g(w) be the first derivative of 3/8*w**4 - s*w**3 + 1/2*w + 1/4*w**2 + 1. Factor g(b).
(b - 1)**2*(3*b + 1)/2
What is h in -15*h + 10*h**2 - 9*h - h**2 - 1 + 13 = 0?
2/3, 2
Let h(s) = s**2 - 5*s - 4. Let g be h(6). Factor -6*d**g + d**2 + 8*d**2 - 12.
3*(d - 2)*(d + 2)
Let v = -2891 - -2893. Let -1/2*k - 1/2*k**v + 0 = 0. Calculate k.
-1, 0
Suppose -3 = 4*m - 15. Let n(l) = -l**2 + 2*l + 1. Let d be n(2). Factor y**4 - 2*y - y**2 + y**2 + d + 2*y**m - 2.
(y - 1)*(y + 1)**3
Let c(l) = l**2 - 6*l - 5. Let r be c(7). Factor -1 + q**r + 0*q**2 + 4*q**2 - 4*q**2.
(q - 1)*(q + 1)
Let z be (23 - 10)/1 - 11. Let -4/5*d + 24/5*d**4 - 26/5*d**z + 9/5*d**5 + 1/5*d**3 + 8/5 = 0. What is d?
-2, -1, 2/3
Let u(l) = 1 + 8 + l - 4 - 6*l**2. Let c(o) = o**2 - 1. Let t be (-4 - -1)*(-4)/(-3). Let b(d) = t*u(d) - 20*c(d). Factor b(s).
4*s*(s - 1)
Let h(d) = -d**4 - 2*d**3 + 11*d**2 - 8*d - 2. Let u(x) = x**4 + 5*x**3 - 23*x**2 + 17*x + 5. Let y(m) = 5*h(m) + 2*u(m). Factor y(k).
-3*k*(k - 1)**2*(k + 2)
Let d(k) be the first derivative of -2*k**5/5 + k**4/2 + 8*k**3/3 - 4*k**2 - 238. Find i such that d(i) = 0.
-2, 0, 1, 2
Factor -3*h**2 + 52*h - 31*h + 3*h**3 - 27*h.
3*h*(h - 2)*(h + 1)
Let z(t) = -t**3 + 11*t**2 - 17*t - 14. Let a be z(6). Factor 4*u + 3*u**2 + 6*u**2 + 2*u - a*u**4 + 61*u**4.
-3*u*(u - 2)*(u + 1)**2
Let n(o) be the first derivative of -5*o**4/2 - 7*o**3/2 - o**2/4 - 65. Factor n(d).
-d*(d + 1)*(20*d + 1)/2
Suppose 17 + 3 = 4*i + 3*j, i - j + 2 = 0. Let h be i/10 - ((-72)/15 - -5). Factor -4/3*w**3 - 2/3 + 4/3*w + h*w**2 + 2/3*w**4.
2*(w - 1)**3*(w + 1)/3
Let k = -58263/5 + 11655. Find j, given that -4/5*j**3 + k*j + 0*j**2 + 8/5 = 0.
-1, 2
Let r(t) be the first derivative of 5*t**4/4 - 55*t**3/9 + 10*t**2 - 20*t/3 - 13. Suppose r(k) = 0. What is k?
2/3, 1, 2
Let z be (3 + -4 - -11) + -1. Suppose -z = -4*j + 11, -4*j = 2*u - 26. Factor -8*n**3 + 2*n**2 - 2*n**u + 0*n**3.
-2*n**2*(5*n - 1)
Let k(l) be the first derivative of -30 + 42*l**2 - l + 15*l + 49*l**3 - 2*l + 0. Factor k(z).
3*(7*z + 2)**2
Suppose 184*s - 83*s + 3*s**3 - 8 - 87*s + 28*s**2 + 3*s**3 = 0. What is s?
-4, -1, 1/3
Let k be (-6 - (-405)/75)/(-1). Find b, given that 12/5*b + 3/5 + k*b**4 + 18/5*b**2 + 12/5*b**3 = 0.
-1
Factor -1309 + 8*w**3 + 4*w**2 + 1309 + 5*w**4 + w**5.
w**2*(w + 1)*(w + 2)**2
Let w(q) be the second derivative of -27*q + 0 + 1/20*q**5 - 1/2*q**2 + 1/2*q**3 - 1/4*q**4. Factor w(l).
(l - 1)**3
Let r = -272 - -157. Let u be r/75 + 20/12. Let -8/15*j**2 + u*j**3 + 2/3*j - 4/15 = 0. What is j?
1, 2
Factor 0 - 204/7*w + 3/7*w**2.
3*w*(w - 68)/7
Let 0 - y**3 + 0*y - 5/4*y**2 = 0. Calculate y.
-5/4, 0
Suppose 3*o - 9 = -3*t, 18*o - 15*o + 23 = 5*t. Let v be (-5)/5 + t/(-20)*-8. Factor -v*x**3 + 12/5*x + 1/5*x**2 - 4/5.
-(x - 2)*(x + 2)*(3*x - 1)/5
Suppose 1/4*n**4 - 13/4*n - 7/4*n**2 + 1/4*n**3 - 3/2 = 0. What is n?
-2, -1, 3
Let z be (-1 + -33*(-3)/72)/3. Let w(d) be the first derivative of -z*d**6 - 1/20*d**5 + 0*d**2 + 0*d + 1/12*d**3 + 3 + 3/16*d**4. Suppose w(b) = 0. What is b?
-1, -1/3, 0, 1
Let p = -20411/36 - -567. Let n(u) be the second derivative of 0 + 0*u**2 + 3*u - 1/9*u**3 + p*u**4. Suppose n(d) = 0. What is d?
0, 2
Let w = 19523/3 + -6505. Find c, given that w - 4/3*c - 4/3*c**2 = 0.
-2, 1
Suppose 0 = -n + 1 + 2. Solve -6*y - 6*y**2 - 7*y + 4*y + 3*y**n = 0 for y.
-1, 0, 3
Let f(r) be the first derivative of -1/12*r**3 + 1/48*r**4 - 3*r - 1 + 1/8*r**2. Let n(o) be the first derivative of f(o). Solve n(b) = 0 for b.
1
Suppose 13 = 21*a - 20*a. Let m(t) = -2*t**3 + 27*t**2 - 14*t + 16. Let b be m(a). Solve 0*s + 0 + 0*s**2 + 1/5*s**b - 1/5*s**4 = 0 for s.
0, 1
Find f, given that -2058 + 147/2*f**5 + 15288*f + 23385/2*f**3 - 63021/2*f**2 - 3171/2*f**4 = 0.
2/7, 7
Suppose 2*a - 8 = 3*a. Let l(w) = -3*w**3 - 5*w**2 - w + 9. Suppose -18 + 8 = 2*n. Let r(x) = 5*x**3 + 8*x**2 + x - 14. Let s(y) = a*l(y) + n*r(y). Factor s(t).
-(t - 1)**2*(t + 2)
Let a(z) be the second derivative of -z**7/21420 + z**6/1020 - 3*z**5/340 - 11*z**4/12 - 7*z. Let m(s) be the third derivative of a(s). Factor m(f).
-2*(f - 3)**2/17
Let a(b) = 6*b**3 + b**2 + b - 2. Let t be a(1). Let r(d) = -d**3 + 7*d**2 - 5*d - 4. Let m be r(t). Find w such that 1/2*w**4 + 0*w - 2*w**m + 0*w**3 + 0 = 0.
-2, 0, 2
Let v(k) = k**2 - 7*k - 3*k**2 + 23*k. Let i(l) = l**2 - 16*l. Let a(z) = 6*i(z) + 5*v(z). Let a(h) = 0. Calculate h.
-4, 0
Let f(i) = -i**2 + 7*i + 3. Let y = 15 + -19. Let z(u) = -6*u - 2. Let b(d) = y*f(d) - 6*z(d). Let b(m) = 0. Calculate m.
-2, 0
Let z = 1067/3 + -5326/15. Determine j, given that -z*j**2 - 9/5 + 12/5*j = 0.
1, 3
Let n(m) be the second derivative of 5*m**7/273 - 2*m**6/195 - m**5/26 + m**4/39 + 5*m + 3. Determine c, given that n(c) = 0.
-1, 0, 2/5, 1
Let a = 443 - 441. Let w(r) be the second derivative of 11/39*r**3 + 2*r - 1/26*r**4 - 6/13*r**a + 0. Find v such that w(v) = 0.
2/3, 3
Let r(w) = -w**3 + 5*w**2 + 7*w + 5. Let g be r(6). Suppose -g = -v - 3*k, k = 6*k - 10. Solve 3*x - 2*x**3 + 93*x**2 + 0*x**3 + v*x**3 - 87*x**2 = 0 for x.
-1, 0
Determine f so that 1/7*f**2 - 8/7*f + 12/7 = 0.
2, 6
Let c(w) = -w**3 + w**2 + 2*w + 2. Let f(n) = -2*n**4 - 6*n**3 - 22*n**2 - 22*n - 12.