3*n - 5*n. Suppose -2/7*u**v - 2/7*u**2 + 0 + 0*u + 2/7*u**5 + 2/7*u**4 = 0. What is u?
-1, 0, 1
Suppose 0 = -4*z + 20, 4*a - 2*z - 7 - 3 = 0. Suppose 3*i - a*c - 4 = 0, 0 = 5*c - 1 - 4. Determine h so that 1/2*h**i - 1/2 + 1/2*h**2 - 1/2*h = 0.
-1, 1
Let p = -3 - -6. Factor -5*u**3 + 6*u**3 - u**4 - u**2 - 3*u**p.
-u**2*(u + 1)**2
Suppose b + 24 = -3*b. Let z be 16/6 + b/9. Factor y**3 + 4*y + z*y**3 - 2*y + 4*y**2 - y**3.
2*y*(y + 1)**2
Let d be 3*1*(-5 + 6). Suppose x = -p, -p = -4*p + d*x + 18. Solve y**3 - 4*y**5 + 0*y**3 - 3*y**p - 6*y**4 = 0.
-1, -1/2, 0
Let a = 2 - 10. Let s be 3/9 + a/(-3). Factor -s + z**2 + 5 - 3*z**2.
-2*(z - 1)*(z + 1)
Suppose 2*m = 3*r - 2*m - 9, -r + 3 = 2*m. Suppose -r*i + i - 2*f = -2, 0 = -3*i - f + 9. Determine z, given that 2 + 4*z**4 - 4*z**2 - 2*z**i + 0 = 0.
-1, 1
Let n = 15769/618 + -5/309. What is i in -15/2*i**5 + n*i**4 - 3*i + 33/2*i**2 + 0 - 63/2*i**3 = 0?
0, 2/5, 1
Suppose -3*a = -0*t - 4*t + 43, -4*a - 24 = -2*t. Let w = 10 - t. Solve 0 + 0*c + 2/7*c**3 + w*c**2 = 0.
0
Suppose 0 = 2*u + p - 3, -3*u + p - 4*p + 6 = 0. Let v be 2*(-2)/(-12)*u. Factor -v*c**4 + 2/3*c - 2/3*c**3 + 1/3 + 0*c**2.
-(c - 1)*(c + 1)**3/3
Let c = 2 + -8. Let v(s) = -s**5 + s**4 + s**3 - 1. Let g(j) = -3*j**5 + 6*j**3 + 6*j**2 - 3*j - 6. Let y(z) = c*v(z) + g(z). Factor y(i).
3*i*(i - 1)**3*(i + 1)
Let u(y) be the first derivative of -y**5/30 + y**3/3 - 3*y**2/2 + 7. Let d(c) be the second derivative of u(c). Let d(b) = 0. Calculate b.
-1, 1
Let r be 2*4 + (-1 - -3). Let v = -4 + r. Let v + 2*l**2 - 6 = 0. What is l?
0
Let x(j) = j**3 + 16*j**2 + 5*j + 84. Let b be x(-16). Solve 1/3*p**5 + 0 + 0*p + p**b + p**3 + 1/3*p**2 = 0.
-1, 0
Let x(y) = y**2 - 8*y + 4. Let j be x(3). Let q be 2/j - (-96)/44. Find s such that -4/7 - 2/7*s**q - 6/7*s = 0.
-2, -1
Let w(b) be the third derivative of b**6/120 - b**5/60 - b**4/24 + b**3/6 - 9*b**2. Determine k, given that w(k) = 0.
-1, 1
What is d in 2/7*d**2 + 0 + 4/7*d = 0?
-2, 0
Let q = 66/25 - 2371/900. Let d(u) be the third derivative of 3*u**2 + q*u**5 + 0*u**3 + 0*u + 1/360*u**6 + 0 - 1/36*u**4. Suppose d(g) = 0. What is g?
-2, 0, 1
Let k(j) be the second derivative of -3/7*j**2 + 9*j - 3/140*j**5 + 0*j**4 + 3/14*j**3 + 0. Determine x so that k(x) = 0.
-2, 1
Let m(p) be the first derivative of -4*p**6/21 + 18*p**5/35 + p**4/7 - 6*p**3/7 + 2*p**2/7 + 28. Let m(b) = 0. Calculate b.
-1, 0, 1/4, 1, 2
Let r(m) be the second derivative of -m**4/6 - m**3 + 10*m**2 + 22*m. Find l such that r(l) = 0.
-5, 2
Let l = 88 - 85. Let -2/3*o**2 + 2/3*o**l + 0 + 0*o = 0. What is o?
0, 1
Let w be (-20)/(-4) + -4 + 2. Let o(r) be the first derivative of -2/5*r + 2/5*r**2 - 2/15*r**w - 1. Factor o(q).
-2*(q - 1)**2/5
Let g(m) be the third derivative of -m**5/90 + 5*m**4/54 - m**3/9 - 6*m**2. Factor g(n).
-2*(n - 3)*(3*n - 1)/9
Suppose 0 = 10*d - 8*d. Let p(t) be the second derivative of 1/21*t**3 - 1/21*t**4 + 0 + 1/70*t**5 + d*t**2 - 3*t. Factor p(y).
2*y*(y - 1)**2/7
Let d be (-84)/56 - (-22)/12. Suppose -j**2 - j**3 + 0 - 1/3*j**4 - d*j = 0. What is j?
-1, 0
Suppose -5*a = -0*a - 15. Factor -3*w**2 + 0*w**2 - 2*w**3 + 3*w**5 - 4*w**4 - w + a*w**2 + 4*w**2.
w*(w - 1)**2*(w + 1)*(3*w - 1)
Let s(f) be the first derivative of 0*f - 5/12*f**6 + 3/2*f**4 - 3/10*f**5 - 6 - 2/3*f**3 + 0*f**2. Find c such that s(c) = 0.
-2, 0, 2/5, 1
Let q(a) = 3*a**2 + a - 1. Let g be q(1). Solve -2*r**g - r + 2*r + 2*r**5 - r = 0 for r.
-1, 0, 1
Let l(b) be the third derivative of b**5/180 + b**4/36 + 4*b**2. Determine z, given that l(z) = 0.
-2, 0
Let m(n) be the third derivative of n**7/105 + 2*n**6/15 + 11*n**5/15 + 2*n**4 + 3*n**3 - 36*n**2. Factor m(g).
2*(g + 1)**2*(g + 3)**2
Let c(y) be the first derivative of 4/5*y + 2/15*y**3 - 2 + 3/5*y**2. Factor c(x).
2*(x + 1)*(x + 2)/5
Let f = 854/585 - 1/65. Let o(w) be the first derivative of 1/15*w**5 - 2*w**2 + 2 + 4/3*w - 1/2*w**4 + f*w**3. Find a, given that o(a) = 0.
1, 2
Let r(g) be the second derivative of 7*g**5/8 - 5*g**4/12 - 21*g. Factor r(f).
5*f**2*(7*f - 2)/2
Let h(t) be the third derivative of t**6/24 - t**5/12 - 5*t**4/24 + 5*t**3/6 + 28*t**2. Factor h(l).
5*(l - 1)**2*(l + 1)
Let d(x) = 1. Let n(l) = 1. Let s(b) = d(b) - 2*n(b). Let h(o) = -2*o**2 + 2*o + 6. Let f(y) = -h(y) - 6*s(y). Factor f(u).
2*u*(u - 1)
Let s = 1 + -5. Let f(v) = v**3 + 4*v**2 - 2*v - 4. Let c be f(s). Factor 0*n**2 - 1/4*n**3 - 1/4*n**5 + 0 + 0*n + 1/2*n**c.
-n**3*(n - 1)**2/4
Suppose -5*w = -4*y + 6, 2*y - 23 + 7 = -4*w. Suppose 5*q + 5*a = -15, -q - w*a = 2*q + 4. Suppose 2/9*o**q + 2/9*o**3 + 0 + 0*o = 0. Calculate o.
-1, 0
Let y(f) be the second derivative of f**8/1680 - f**7/840 - f**6/360 + f**5/120 - 7*f**3/6 + 7*f. Let i(j) be the second derivative of y(j). Factor i(h).
h*(h - 1)**2*(h + 1)
Let d = -107/4 - -27. Suppose d*i + 1/2 - 1/4*i**3 - 3/4*i**2 + 1/4*i**4 = 0. What is i?
-1, 1, 2
Let u be -8 + 5 - 2368/14. Let a = 173 + u. Find w such that -a*w**4 + 10/7*w**5 + 6/7*w**2 - 2*w**3 + 0 + 4/7*w = 0.
-1, -2/5, 0, 1
Let m(a) be the first derivative of 0*a + 0*a**3 + 0*a**2 - 1/8*a**4 + 3/10*a**5 + 1/3*a**6 - 3. Factor m(f).
f**3*(f + 1)*(4*f - 1)/2
Factor -1/2*x**3 + 4*x**2 - 10*x + 8.
-(x - 4)*(x - 2)**2/2
Let g = 112 + -279. Let t = 1505/9 + g. Let -4/9*p + 8*p**3 - t + 10/3*p**2 = 0. Calculate p.
-1/3, 1/4
Let r(s) be the first derivative of -8*s**5/5 - 25*s**4 - 332*s**3/3 - 48*s**2 + 144*s + 27. Let r(d) = 0. What is d?
-6, -1, 1/2
Let r(c) = 2*c**2 - 10*c - 9. Let d(p) = -p**2 + p + 1. Let k(w) = -3*d(w) - r(w). Let k(v) = 0. What is v?
-6, -1
Let y(w) be the third derivative of -w**7/70 + w**6/20 + 3*w**5/20 - w**4 + 2*w**3 - 10*w**2. Factor y(d).
-3*(d - 2)*(d - 1)**2*(d + 2)
Let t = -53 + 377/7. Factor 6/7*f - t*f**3 + 0 + 3/7*f**2 - 3/7*f**4.
-3*f*(f - 1)*(f + 1)*(f + 2)/7
Let c = 1028 + -1024. Factor 0 + 0*t - 2/9*t**c + 2/9*t**3 + 4/9*t**2.
-2*t**2*(t - 2)*(t + 1)/9
Let g = 20 + -40. Let v = g + 23. Factor 1/2 + 0*u**v - u**2 + 0*u + 1/2*u**4.
(u - 1)**2*(u + 1)**2/2
Let i be (-7 - -5) + (0 - -6). Let x be 62/28 + (-2)/i. Suppose x*a - 16/7*a**2 - 2/7 = 0. Calculate a.
1/4, 1/2
Suppose -28/5*s - 8/5*s**2 - 16/5 + 4/5*s**3 = 0. Calculate s.
-1, 4
Let p(c) = 5*c**2 - 2. Let l(r) = 1. Let g(h) = -2*l(h) - p(h). Determine d, given that g(d) = 0.
0
Determine q, given that 80*q**2 - 55*q**4 + 6 - 6 + 15*q**5 + 20*q + 115*q**3 + 125*q**4 = 0.
-2, -1, -2/3, 0
Suppose 2*u - 4 = -0*u. Suppose -5*d + 57 = 7. Factor -9*g - 8*g + 2 + 8*g**u + 4*g + d*g**2.
(2*g - 1)*(9*g - 2)
Let v = 6 - 6. Let w = -67/3 + 25. Factor v - 1/3*y - 11/6*y**2 - w*y**3 - 7/6*y**4.
-y*(y + 1)**2*(7*y + 2)/6
Let z(d) = 20*d**5 - 30*d**4 + 65*d**3 - 75*d**2 + 5*d - 15. Let v(o) = o**5 - o**2 - o - 1. Let a(s) = 15*v(s) - z(s). Factor a(i).
-5*i*(i - 2)**2*(i - 1)**2
Let f(l) be the first derivative of 0*l + 0*l**3 + 1/13*l**2 - 1/26*l**4 - 6. Factor f(d).
-2*d*(d - 1)*(d + 1)/13
Suppose 0*f + 13 = 5*f - 3*v, -f - 3*v - 1 = 0. Let h = 697/12 + -172/3. Factor 0 + 0*z**f + 0*z - 3/4*z**3 - 3/2*z**4 - h*z**5.
-3*z**3*(z + 1)**2/4
Let m(x) be the first derivative of -4 + 0*x + 1/6*x**4 - 2/3*x**2 + 1/9*x**6 - 2/5*x**5 + 2/3*x**3. Solve m(u) = 0 for u.
-1, 0, 1, 2
Let x(v) = -2*v - 2. Let w be x(-4). Determine n so that n**4 - 9*n**4 + w*n**3 - n**4 - 3*n**5 + 6*n**5 = 0.
0, 1, 2
Let u(q) be the first derivative of -4 - 6*q**4 + 4/5*q**5 + 12*q**3 + 0*q**2 + 0*q. Factor u(j).
4*j**2*(j - 3)**2
Let h(s) be the second derivative of s**7/357 - s**5/85 + s**3/51 + 8*s. Factor h(u).
2*u*(u - 1)**2*(u + 1)**2/17
Suppose -a - 4 = -3*g - 0*a, 5*a = -20. Factor 1/3*q**2 + g + 2/3*q.
q*(q + 2)/3
Let p(h) be the third derivative of 0*h**3 + 0*h + 0 + 1/30*h**5 + h**2 + 1/12*h**4. Factor p(q).
2*q*(q + 1)
Let x(z) = -3*z**2 + 2*z + 2. Let u(l) = -l - 8. Let q be u(-7). Let y be q*3/6*-2. Let h(s) = s**2 - 1. Let m(f) = y*x(f) + 2*h(f). Factor m(t).
-t*(t - 2)
Factor 8*y - 8*y**3 + 7*y**4 - y**4 - 2*y**4 - 4.
4*(y - 1)**3*(y + 1)
Suppose 35 = -3*m + 8*m. Let y(c) be the third derivative of 0*c + 0*c**3 - 1/480*c**6 - 1/240*c**5 + 1/1344*c**8 + 0*c**4 + 1/840*c**m + c**2 + 0. Factor y(w).
w**2*(w - 1)*(w + 1)**2/4
Let z(p) = p**2 + 4. Let l(w) = -w**2 - 5. Let h(r) = 2*l(r) + 3*z(r). Let u be h(0). Factor -5/2*y**5 