 + 1)*(p + 2)**2/5
Let w = -21 + 45/2. Let i be (-1)/(-3)*(-3)/(-2). Factor -i*c**3 - 3/2*c**2 - 1/2 - w*c.
-(c + 1)**3/2
Suppose -5*v + 0*v = -15. Let w(d) = -d**2 + 6*d + 31. Let z be w(9). Factor 1/3*r + 0 - 1/3*r**2 + 1/3*r**z - 1/3*r**v.
r*(r - 1)**2*(r + 1)/3
Suppose 2*q = -3 + 13. Solve -6*n - 4*n**4 + 4*n**2 - 2*n**4 + 6*n**q + 4*n**3 - 4*n**5 + 0 + 2 = 0.
-1, 1
Let b be -1 - (5 + -2) - 7. Let t be (-10 - b) + 2/(-3). Factor -t*l**4 + 0*l + 0 + 4/3*l**3 - 4/3*l**2.
-l**2*(l - 2)**2/3
Let w(f) = 2*f**4 + 0*f**3 + 5*f - f**4 - 6*f - f**3. Let x(b) = 4*b**4 + 2*b**3 + 2*b**2 - 2*b. Let h(v) = -2*w(v) + x(v). Suppose h(q) = 0. What is q?
-1, 0
Let v(x) be the first derivative of -12*x**5/5 + 2*x**4 + 4*x**3 - 4*x**2 - 9. Find u such that v(u) = 0.
-1, 0, 2/3, 1
Let v = 12 - 7. Let g(b) be the first derivative of 0*b + 2/15*b**v - 2 + 0*b**2 - 1/6*b**4 + 0*b**3. Factor g(d).
2*d**3*(d - 1)/3
Let u(q) be the first derivative of q**7/6720 + q**6/1440 + q**5/960 + 3*q**3 + 6. Let i(b) be the third derivative of u(b). Factor i(g).
g*(g + 1)**2/8
Factor 0 + 0*j - 5/3*j**2 + 5/3*j**3.
5*j**2*(j - 1)/3
Let u(n) be the third derivative of n**8/448 - n**7/140 - n**6/160 + n**5/40 + 3*n**2. Determine m, given that u(m) = 0.
-1, 0, 1, 2
Let 2/3*f + 2*f**2 + 2*f**3 + 2/3*f**4 + 0 = 0. What is f?
-1, 0
Let t(n) be the second derivative of n**10/30240 - n**9/15120 - n**4/4 - 2*n. Let l(f) be the third derivative of t(f). Solve l(z) = 0 for z.
0, 1
Let o(b) be the third derivative of -1/2*b**3 - 1/20*b**5 + 0*b + 1/4*b**4 + 0 - 10*b**2. Factor o(t).
-3*(t - 1)**2
Let p(t) be the second derivative of t**6/360 + t**5/40 + t**4/12 - t**3/3 - 5*t. Let x(s) be the second derivative of p(s). Factor x(i).
(i + 1)*(i + 2)
Find b such that 16*b**2 - 22*b**2 + 2*b**4 + 2*b**3 + 7*b**2 - b**4 = 0.
-1, 0
Let u(l) = l**3 + 12*l**2 - 30*l - 28. Let p be u(-14). Suppose p*m**4 + 0*m**3 + 0 + 1/3*m**5 + 0*m + 0*m**2 = 0. Calculate m.
0
Solve -4/5*j**2 - 4/5*j + 0 = 0.
-1, 0
Let c(s) = -4*s**2 + 2*s + 5. Suppose -5 = 2*z + 29. Let r(m) = 12*m**2 - 5*m - 14. Let t(q) = z*c(q) - 6*r(q). Solve t(n) = 0 for n.
-1/2
Let g(x) be the third derivative of -x**5/150 + 2*x**4/15 - 16*x**3/15 + 3*x**2. Let g(z) = 0. Calculate z.
4
Let a(y) = -y + 14. Let x = 9 - -4. Let i be a(x). Solve 0*o - 1/4*o**3 - 3/4*o**2 + i = 0 for o.
-2, 1
Solve -52*q**4 + 467*q**5 - 116*q**2 - 118*q**4 - 417*q**5 + 212*q**3 + 26*q - 2 = 0 for q.
1/5, 1
Let g = -13 + 10. Let r = -3 - g. Determine p, given that 1/4*p**3 + 0 + 1/4*p**4 + 0*p + r*p**2 = 0.
-1, 0
Suppose 9 = 12*v - 9*v. Let t(l) be the first derivative of 1 - l**2 + l + 1/3*l**v. Solve t(w) = 0.
1
Suppose w - 12 = -5*r, 12 + 0 = 3*r + 3*w. Find c, given that -2 - r*c - 1/2*c**2 = 0.
-2
Determine o so that -3/2*o**5 + 0*o**2 + 6*o**4 + 0*o + 0 - 9/2*o**3 = 0.
0, 1, 3
Let o(m) = -m**2 + 17*m - 9. Let v(l) = -4*l + 2. Let s be (0 + 3)*4/(-6). Let i(q) = s*o(q) - 9*v(q). Factor i(k).
2*k*(k + 1)
Let a = -16 - -41. Let i = a + -25. What is s in 16/11*s**3 + 2/11*s + i + 12/11*s**2 = 0?
-1/2, -1/4, 0
Factor 0 - 2*s - 7/2*s**4 - 23/2*s**3 - 10*s**2.
-s*(s + 1)*(s + 2)*(7*s + 2)/2
Let x(i) be the second derivative of -1/4*i**4 - 1/28*i**7 - 3/8*i**5 + 0*i**3 - 1/5*i**6 - i + 0*i**2 + 0. Factor x(k).
-3*k**2*(k + 1)**2*(k + 2)/2
Find n, given that -4*n**4 + 8*n**3 - 3401 + 4*n**2 + 3401 - 8*n = 0.
-1, 0, 1, 2
Solve 2*v + 2*v - 48*v**3 - 8*v**2 + 8 + 44*v**3 = 0.
-2, -1, 1
Let n be (7/(-1050))/(12/(-10)). Let z(l) be the third derivative of 0 + n*l**6 + 0*l**3 + 0*l**5 + 0*l**4 - 2*l**2 + 0*l - 1/315*l**7. What is x in z(x) = 0?
0, 1
Let t(v) = -v**2 + 10*v + 13. Let z be t(11). What is r in -6*r**3 - 2*r**3 - 2 - 4*r**4 + r**2 + 5*r + 0*r**3 + 3*r**5 + 5*r**z = 0?
-1, 1/3, 1, 2
Suppose 2*x + 2 - 6 = 0. Suppose -5*w + 9 = -x*w. Determine u, given that 0*u**2 + 2*u**4 - u**2 - u**2 - 4*u**w + 4*u**2 = 0.
0, 1
Let k be (-16)/(-156)*(-6 + -1). Let f = 18/13 + k. What is r in 0*r - 2/3*r**3 - f*r**2 + 0 + 2/3*r**5 + 2/3*r**4 = 0?
-1, 0, 1
Let c be 155/10 + 1/4. Let k = c + -57/4. Factor 0 + 2*q**2 - k*q**3 - 1/2*q.
-q*(q - 1)*(3*q - 1)/2
Let g(y) be the third derivative of -3*y**7/14 + y**6 - 11*y**5/6 + 5*y**4/3 - 5*y**3/6 - 12*y**2. Factor g(n).
-5*(n - 1)**2*(3*n - 1)**2
Let g(b) be the second derivative of -2*b + 0 - 7/9*b**3 - 4/9*b**4 - 1/3*b**2 + 8/15*b**5. Factor g(l).
2*(l - 1)*(4*l + 1)**2/3
Suppose 3*m = 5*b - 97, -b + 0*b - 2*m = -22. Factor 20*q - b*q - 8*q**4 - 2*q**2 - 10*q**3.
-2*q**2*(q + 1)*(4*q + 1)
Let -36/5 - 1/5*a**2 - 12/5*a = 0. What is a?
-6
Let t(j) = j**4 + j**2 - j + 1. Let p(n) = 5*n**4 + n**3 + 9*n**2 - 7*n + 4. Let k(w) = -p(w) + 6*t(w). Factor k(y).
(y - 2)*(y - 1)*(y + 1)**2
Factor 0 - 8/5*l**3 - 2*l**2 - 2/5*l**4 - 4/5*l.
-2*l*(l + 1)**2*(l + 2)/5
Let q = 15/14 + -9/28. Factor 1/2 + 1/4*k**2 + q*k.
(k + 1)*(k + 2)/4
Let u be ((-3)/(-6) + 1)/(-81). Let z = u + 113/270. Factor -1/5*n**3 - z*n**2 - 1/5*n + 0.
-n*(n + 1)**2/5
Let x(i) = -4*i**2 - 4*i - 3. Let j be -7 + 4 + -1 + 2. Let l = -4 - j. Let v(f) = 3*f**2 + 3*f + 2. Let p(g) = l*x(g) - 3*v(g). Factor p(c).
-c*(c + 1)
Suppose 3*v - 107 + 29 = 0. Suppose -5*t - 5*s + 2 = -28, -5*t - 4*s + v = 0. Factor -2*u - 3*u**2 - 2*u**2 + 3*u**t.
-2*u*(u + 1)
Determine q, given that 3/5*q - 1/5*q**3 - 2/5 + 0*q**2 = 0.
-2, 1
Let s(g) be the second derivative of -g**6/10 - 3*g**5/20 + g**4/4 + g**3/2 - 9*g. Factor s(b).
-3*b*(b - 1)*(b + 1)**2
Let f(z) = -45*z**2 + 24*z - 3. Let o(l) = l**2. Let b(m) = f(m) - 3*o(m). Factor b(p).
-3*(4*p - 1)**2
Let y be 1/(23/(-6) + 4). Let l be 18/y - 57/27. What is c in -8/9*c + 2/9*c**2 + l = 0?
2
Let m(p) be the second derivative of 3/130*p**5 + 2/39*p**4 - 2/13*p**2 - 1/39*p**3 + 0 - 4*p. Factor m(a).
2*(a + 1)**2*(3*a - 2)/13
Let n = -4613/9 - -513. Factor 2/9 - 2/9*x**4 - n*x**3 + 0*x**2 + 4/9*x.
-2*(x - 1)*(x + 1)**3/9
Let q(c) be the third derivative of c**8/1848 - c**6/330 + c**4/132 - 4*c**2. Solve q(p) = 0 for p.
-1, 0, 1
Let o be 2 - (3 - 527/525). Let c(b) be the third derivative of 0*b**4 + 0 + 0*b**3 + 0*b**5 + b**2 - o*b**7 + 0*b - 1/600*b**6. Suppose c(n) = 0. Calculate n.
-1/4, 0
Let z be 35/20 + (-3)/2. Factor -f + z*f**2 + 3/4.
(f - 3)*(f - 1)/4
Let h(y) = -3*y**4 - 9*y**3 - 5*y**2 + 4*y - 2. Let u(c) = c**4 + 4*c**3 + 2*c**2 - 2*c + 1. Let d(f) = 2*h(f) + 5*u(f). Factor d(p).
-(p - 1)**3*(p + 1)
Suppose 4*f = 16, -f = 6*x - 2*x - 12. Factor 0 - 2/3*o**3 - 2/9*o**5 + 0*o - 2/3*o**4 - 2/9*o**x.
-2*o**2*(o + 1)**3/9
Factor 18/11*x**4 - 4/11 - 50/11*x**3 - 6/11*x + 42/11*x**2.
2*(x - 1)**3*(9*x + 2)/11
Suppose 3*w + 5*h = 4*h - 126, 4*w = -3*h - 173. Let q = w + 125/3. Solve q*x**3 + 4/3*x**2 + 2/3*x + 0 = 0.
-1, 0
Let h(v) be the first derivative of -243*v**4/4 - 36*v**3 - 6*v**2 - 4. Factor h(q).
-3*q*(9*q + 2)**2
Let y(z) = z. Let f(t) = 2. Let h(x) = f(x) + y(x). Let o be h(0). Suppose -10*g - g**3 - 20*g**2 - 10*g**4 - o*g**5 - 19*g**3 - 2 + 0 = 0. What is g?
-1
Suppose -n - 2*n = 2*c - 12, -53 = -5*c + 4*n. Let g be 3/c + (-16)/(-6). Find q such that -3/4*q + 3/2*q**g - 1/2 - 3/4*q**5 + q**2 - 1/2*q**4 = 0.
-1, -2/3, 1
Let l(p) be the second derivative of p**6/900 - p**5/150 + p**4/60 - 2*p**3/3 - 7*p. Let t(x) be the second derivative of l(x). Factor t(c).
2*(c - 1)**2/5
Let m(a) be the second derivative of -3*a - 1/42*a**4 - 4/21*a**3 + 0 - 4/7*a**2. Determine u, given that m(u) = 0.
-2
Let h(a) = -51*a**4 - 49*a**3 + 91*a**2 + 49*a - 40. Let k(p) = 10*p**4 + 10*p**3 - 18*p**2 - 10*p + 8. Let s(d) = -2*h(d) - 11*k(d). Let s(j) = 0. What is j?
-2, -1, 1/2, 1
Let a(l) be the third derivative of -3*l**2 + 0*l**3 - 2/525*l**7 + 0*l + 0*l**4 + 0 + 0*l**5 + 1/300*l**6 + 1/840*l**8. Factor a(q).
2*q**3*(q - 1)**2/5
Let n be ((-234)/65)/(8/110). Let x = n - -54. Solve -6*s**2 + 21/2*s - x = 0 for s.
3/4, 1
Let v(p) = 2*p**2 - 4*p + 2. Let h(w) = -3*w**2 + 4*w - 3. Let u(o) = -7 - 1 + 3*o - 4*o. Let c be u(-4). Let x(d) = c*h(d) - 5*v(d). What is q in x(q) = 0?
-1
Let g = 14 - 15. Let r = 1 - g. Factor 4/3*z**r - 4/3 - 2/3*z**3 + 2/3*z.
-2*(z - 2)*(z - 1)*(z + 1)/3
Let i(y) = 6*y**3 - 17*y**2 - 5*y + 10. Let w be i(3). Factor 0*x + 0*x**2 + 2/7*x**5 + 0*x**w + 0 - 2/7*x**3.
2*x**3*(x - 1)*(x + 1)/7
Let o(s) be the first derivati