2*a**3 - 24*a**5 - 3*a**5 - 251*a**3 + 33*a**4 + 6*a = 0. What is a?
-1, 0, 2/9, 1
Determine h, given that 3*h**4 + 5*h**3 + 0*h**3 + h**2 - 2*h**3 + h**5 = 0.
-1, 0
Let r(f) = -3*f**3 - f**2 - 2*f - 1. Let x be r(-1). Factor -81*u**x - 5*u - 54*u**5 - 162*u**4 - 88*u**2 - 11*u - 99*u**3.
-2*u*(u + 1)*(3*u + 2)**3
Let j(w) be the first derivative of -w**2/2 - 8*w - 2. Let z be j(-8). Factor z - 2/3*h - 1/3*h**2.
-h*(h + 2)/3
Let v = 43/204 + -3/68. Determine u so that 1/6*u**2 + 0 + v*u = 0.
-1, 0
Factor 5*b**2 - 10*b - 16*b**2 + 13*b**2 + 8.
2*(b - 4)*(b - 1)
Let x = 29 - 19. Suppose -11*l = -x*l. Find r, given that 0*r + 14/3*r**5 + 10/3*r**3 + l - 4/9*r**2 - 68/9*r**4 = 0.
0, 2/7, 1/3, 1
Let y = 3/8 - 1/24. Suppose -1/3*p**2 + y*p**3 + 0 - 2/3*p = 0. What is p?
-1, 0, 2
Let i(q) = -5*q**2 + 20*q - 27. Let v(s) be the first derivative of 17*s**3 - 201*s**2/2 + 270*s - 3. Let k(g) = 21*i(g) + 2*v(g). Factor k(y).
-3*(y - 3)**2
Factor 1/4*m**4 - 1/4*m + 0 + 3/4*m**2 - 3/4*m**3.
m*(m - 1)**3/4
Let m be 52/(-65) - 2/(-2). Determine q, given that 1/5*q**2 - m*q - 2/5 = 0.
-1, 2
Let p be 26/8 - ((-42)/(-8) + -5). Let l(t) be the third derivative of -1/70*t**5 + 0*t - 1/420*t**6 + 0 - 1/28*t**4 - 1/21*t**p - 4*t**2. Factor l(u).
-2*(u + 1)**3/7
Let t = 4411/45 - 98. Let k(m) be the second derivative of 0 + 1/135*m**6 + 0*m**2 + 0*m**3 - 2*m + t*m**5 + 1/54*m**4. Factor k(n).
2*n**2*(n + 1)**2/9
Let h(w) be the third derivative of -w**8/10080 + w**5/15 + 8*w**2. Let b(r) be the third derivative of h(r). Suppose b(l) = 0. Calculate l.
0
Let k(f) be the first derivative of -f**4/30 + f**2/5 + 4*f/15 + 20. Factor k(a).
-2*(a - 2)*(a + 1)**2/15
Solve k**5 - 3*k**5 - 6*k + 8*k**4 - 12*k + 3*k**3 - 24*k**2 + k**3 = 0 for k.
-1, 0, 3
Factor -48/7*u**2 + 4/7*u + 0 + 144/7*u**3.
4*u*(6*u - 1)**2/7
Factor -6*x + 2*x**3 + 3*x - 3*x**3 - x**2 + 5*x.
-x*(x - 1)*(x + 2)
Let l = -18/11 - -101/55. Solve l*d**2 + 1/5 - 2/5*d = 0 for d.
1
Let y(u) be the second derivative of -u**5/150 - u**4/30 - u**3/15 - u**2 + u. Let g(z) be the first derivative of y(z). Factor g(o).
-2*(o + 1)**2/5
Solve -24*o**2 - 16/7*o - 84*o**3 + 0 - 98*o**4 = 0.
-2/7, 0
Let v(a) be the third derivative of 1/60*a**5 + 1/24*a**4 + 0*a**3 + 0*a - 1/210*a**7 - 1/120*a**6 + a**2 + 0. Factor v(r).
-r*(r - 1)*(r + 1)**2
Factor -3*n + 10*n**2 - 15 - 14*n**2 + 9*n**2 - 7*n.
5*(n - 3)*(n + 1)
Let v(a) be the first derivative of a**3/2 + 3*a**2/2 + 3*a/2 - 7. Let v(z) = 0. What is z?
-1
Factor 3*l**5 - 6*l**3 + 3*l - 3*l + 3*l.
3*l*(l - 1)**2*(l + 1)**2
Let y(n) be the third derivative of -n**5/240 + 5*n**4/48 - 25*n**3/24 + 9*n**2. Suppose y(k) = 0. What is k?
5
Let t be 400/(-105)*(-2)/(-10). Let g = -2/21 - t. Find o such that -g*o**3 - 4/3*o**2 + 0 - 2/3*o = 0.
-1, 0
Suppose q + 12 = -5*t, 2*q + 3*t - t = 0. Let g(x) = -x**2 + 4*x. Let c be g(q). Find u, given that 2*u**3 - c*u**2 + 3*u**2 - 2*u**5 = 0.
-1, 0, 1
Let d = 6 + -6. Factor -t**2 - 1/4*t + d.
-t*(4*t + 1)/4
Solve -8/7*t**4 - 2/7 + 20/7*t**3 - 16/7*t**5 + 10/7*t**2 - 4/7*t = 0.
-1, -1/2, 1/2, 1
Suppose -7*r = -6*r - 3. Let y(o) be the second derivative of 0*o**2 + 1/70*o**5 + 1/21*o**r + 0 - 1/21*o**4 + o. Factor y(f).
2*f*(f - 1)**2/7
Let o(r) be the third derivative of r**8/336 - r**6/60 + r**4/24 - 7*r**2. Factor o(w).
w*(w - 1)**2*(w + 1)**2
Let q(j) = -5*j**2 + 325*j - 725. Let s(c) = c**2 - 54*c + 121. Let d(u) = -4*q(u) - 25*s(u). Factor d(n).
-5*(n - 5)**2
Solve -8 - 3/2*b**2 - 13*b = 0.
-8, -2/3
Let t = -2 - -5. Suppose -3*k = 4*i - 20, -2*k + 2 = -6*i + t*i. Factor w**3 + 11*w**k - 2*w - 8*w**2 + w**3 - 3*w**4.
2*w*(w - 1)*(w + 1)*(4*w + 1)
Suppose -m = 4*m - 3*z + 62, -2*m + 4*z - 36 = 0. Let r = m + 10. Factor 0 + 0*c + r*c**2 - 2/3*c**3.
-2*c**3/3
Let b(j) be the first derivative of j**7/840 + j**6/360 + j**3 + 5. Let a(v) be the third derivative of b(v). Let a(k) = 0. Calculate k.
-1, 0
Let b(p) be the second derivative of -p**7/168 + p**5/20 - p**4/24 - p**3/8 + p**2/4 - 9*p. Factor b(q).
-(q - 1)**3*(q + 1)*(q + 2)/4
Suppose -2*l - 8 + 33 = 5*z, 0 = -4*l - z + 5. Suppose -4/7*p**2 - 4/7*p + l + 3/7*p**3 = 0. Calculate p.
-2/3, 0, 2
Let q = -4 + 6. Let o(t) be the third derivative of 0*t**4 + 0 - 1/20*t**5 + 3*t**q + 0*t + 0*t**3. Suppose o(i) = 0. What is i?
0
Let y(f) = 2*f**4 + 3*f**3 - 4*f**2 + 5. Let a(n) = -4*n**4 - 5*n**3 + 8*n**2 - 9. Let i(l) = -3*a(l) - 5*y(l). Solve i(j) = 0 for j.
-1, 1
Let q(x) be the third derivative of -x**8/168 - 4*x**7/105 - x**6/10 - 2*x**5/15 - x**4/12 + 16*x**2. Factor q(y).
-2*y*(y + 1)**4
Suppose -u = -4*u + 15. Determine m, given that 9*m**u + m**2 - 7*m**4 - 9*m**3 + m - 4*m**4 - 13*m**5 - 2*m**2 = 0.
-1, 0, 1/4
Let x = -5357/12 + 447. Let t(b) be the first derivative of -1 + 2/3*b - 2/9*b**3 + x*b**4 - 7/6*b**2. Solve t(p) = 0 for p.
-1, 2/7, 1
Suppose 3*w - 5 = 1. Suppose -w*l**2 + l - 2*l**4 - l**5 + 4*l**2 + l**3 - l**3 = 0. What is l?
-1, 0, 1
Let q(f) be the second derivative of -f**9/8820 - f**8/1680 + f**6/315 - f**4/4 + f. Let v(m) be the third derivative of q(m). Determine a so that v(a) = 0.
-2, -1, 0, 2/3
Let u(x) = 2*x**2 + 4. Let z(o) = 2 + 3 - 1 - 5 - o. Let t(n) = u(n) + 4*z(n). Factor t(p).
2*p*(p - 2)
Let v = 21 + -12. Let w be 1/(-2)*(-4)/v. Factor 0 - w*b**2 - 2/9*b.
-2*b*(b + 1)/9
Let y(r) be the second derivative of -r**6/360 - r**5/80 + r**4/144 + r**3/24 - 56*r. Factor y(u).
-u*(u - 1)*(u + 1)*(u + 3)/12
Let u(h) be the second derivative of -h**5/10 + h**4/6 + 2*h**3/3 + 2*h. Factor u(g).
-2*g*(g - 2)*(g + 1)
Let f(s) be the first derivative of -s**3/2 - 3*s**2 - 9*s/2 - 1. Factor f(v).
-3*(v + 1)*(v + 3)/2
Let g = -9 - -8. Let l be (-7 + 6/2)/g. Factor 0*x + 1/3*x**l + 0 + 1/3*x**2 + 2/3*x**3.
x**2*(x + 1)**2/3
Let f(p) be the third derivative of 0 + 1/60*p**4 + 0*p + 1/1050*p**7 - 2*p**2 - 1/30*p**3 + 0*p**5 - 1/300*p**6. Factor f(y).
(y - 1)**3*(y + 1)/5
Let g(f) be the third derivative of f**5/20 + f**4/4 + f**3/2 + 6*f**2. Let g(d) = 0. Calculate d.
-1
Let -3*q**4 - 8*q + 15*q**4 - 4*q**4 + 12*q**2 - 12*q**4 = 0. Calculate q.
-2, 0, 1
Let g(y) be the third derivative of y**6/180 - y**4/12 - y**3 - 3*y**2. Let p(q) be the first derivative of g(q). Solve p(o) = 0.
-1, 1
Let b(i) be the second derivative of i**7/231 - i**5/55 + i**3/33 - 6*i. Let b(f) = 0. Calculate f.
-1, 0, 1
Factor -1/5*z**4 + 4/5*z**3 - 3/5*z**2 + 4/5 - 4/5*z.
-(z - 2)**2*(z - 1)*(z + 1)/5
Let k(b) be the first derivative of -2*b**5/25 + b**4/2 - 2*b**3/15 - 21*b**2/5 + 36*b/5 + 31. Determine u, given that k(u) = 0.
-2, 1, 3
Factor -64*d**2 - 60*d**2 + 2*d + 123*d**2 - 1.
-(d - 1)**2
Let l(j) = -6*j**4 - 17*j**3 + 12*j + 11. Let b(p) = 3*p**4 + 8*p**3 - 6*p - 5. Let h(s) = 5*b(s) + 2*l(s). Factor h(f).
3*(f - 1)*(f + 1)**3
Let j be (-56)/20*(2 + 3). Let r = j + 16. Solve 0 - 1/4*z**3 + 1/4*z + 0*z**r = 0 for z.
-1, 0, 1
Let i(d) be the second derivative of -d**4/48 - d**3/4 - 9*d**2/8 + 3*d. Factor i(u).
-(u + 3)**2/4
Suppose 0 = 5*f - f + 3*s - 1, -s = -3*f + 17. Solve 0 - 3/4*p**3 - 1/2*p**2 + 5/4*p**f + 0*p = 0.
-2/5, 0, 1
Find p such that 2/5*p**2 - 4/5 + 2/5*p = 0.
-2, 1
Suppose 0 = -3*t + 4 + 2. Factor -5*u + 6*u + 3*u**3 + 2*u**4 - t*u.
u*(u + 1)**2*(2*u - 1)
Let z be 2/(-2) - (-4)/4. Suppose 2*v + v = z. Solve -y + y**3 - 2*y - 2 + v*y**3 + 4 = 0.
-2, 1
Let u be (3/(-6))/((-4)/144). Let x be (-40)/(-18) - 4/u. Determine d, given that -d**4 - 4 + 4*d**3 + 1 + 4 - x + 4*d - 6*d**2 = 0.
1
Let y(n) = -2*n**2 + 2*n. Let v(p) = p**2 - 2*p + 1. Let a(s) = 3*v(s) + 2*y(s). Suppose a(c) = 0. What is c?
-3, 1
Let f(c) = -c**3 - 9*c**2 - c - 3. Let o be f(-9). Suppose -o*d = -8*d. Determine x, given that 1/2*x**4 + 0*x**3 - x**2 + 1/2 + d*x = 0.
-1, 1
Let o(h) be the first derivative of 343*h**6/3 - 588*h**5/5 - 259*h**4/2 + 572*h**3/3 - 84*h**2 + 16*h - 77. Let o(x) = 0. Calculate x.
-1, 2/7, 1
Let k be -3 - (-5 - 1) - (-1)/(-1). Let t(l) be the first derivative of 0*l - 1/2*l**4 + 0*l**3 - 3 + l**k. Let t(c) = 0. Calculate c.
-1, 0, 1
Let n(f) be the third derivative of 3*f**6/100 - 2*f**5/25 - f**4/20 + 2*f**3/5 - 14*f**2. Factor n(s).
6*(s - 1)**2*(3*s + 2)/5
Let m(j) be the second derivative of 9/20*j**5 + 11/20*j**6 + 0 + 3/28*j**7 - 2*j**3 - 3/2*j**4 + 0*j**2 - 6*j. Suppose m(b)