Suppose 4*q + 14 = -3*o, 3*o - 5*q = -3*q + 16. Let i(m) = o*s(m) - 7*c(m). Factor i(x).
(x - 2)*(x + 1)
Determine w so that -34*w + 13*w + 3*w**4 + 0 + 6 + 27*w**2 - 15*w**3 = 0.
1, 2
Let c(b) be the third derivative of 0*b**3 + 1/84*b**4 - 2*b**2 + 0 + 0*b**5 + 0*b - 1/420*b**6. Find t, given that c(t) = 0.
-1, 0, 1
Factor 3/5 + 18/5*z**2 - 12/5*z - 12/5*z**3 + 3/5*z**4.
3*(z - 1)**4/5
Let p(d) be the third derivative of -2*d**2 + 1/24*d**3 + 1/240*d**5 + 1/48*d**4 + 0 + 0*d. Factor p(x).
(x + 1)**2/4
Suppose -4*r = -5*r + 2*b, 4*r + 5*b = 0. Suppose r = 2*v - 4*v. Factor -6*s**2 + 4*s**3 + v*s**2 - s**4 + 2*s**2.
-s**2*(s - 2)**2
Let v(a) = 2 + 4*a**3 + 1 + 5*a**2 - 1 - 3*a**3. Let d be v(-5). Factor -d*g**3 + 2*g**4 + 0*g**2 + 10*g + 0*g**3 - 4*g**4 + 4 + 6*g**2.
-2*(g - 2)*(g + 1)**3
Let q = 4 + -1. Suppose -6 = q*i - 6*i. Factor 2*x - i*x + 4*x - 2*x**2 - 2.
-2*(x - 1)**2
Let b = 133 + -131. Let m(n) be the first derivative of 0*n - 1/2*n**4 + 0*n**b + 1/3*n**3 + 1/5*n**5 - 3. Factor m(q).
q**2*(q - 1)**2
Let z(h) be the first derivative of 4*h**5/5 + 3*h**4 + 4*h**3 + 2*h**2 - 1. Factor z(t).
4*t*(t + 1)**3
Let v(u) be the third derivative of 3*u**2 + 0*u**5 + 1/60*u**6 - 1/210*u**7 + 0*u - 1/12*u**4 + 1/6*u**3 + 0. Find l such that v(l) = 0.
-1, 1
Suppose g + 468 = 67. Let f = g - -3623/9. Factor -2/9*j**5 - 38/9*j**3 - 50/9*j**2 - f*j**4 - 32/9*j - 8/9.
-2*(j + 1)**3*(j + 2)**2/9
Let f be 105/14 + (-2)/4. Determine o, given that 2*o**5 - 4*o**3 + f*o + 4*o**2 + 6 - 2*o**4 - 8 - 5*o = 0.
-1, 1
Let t(r) be the second derivative of 1/6*r**3 + 0*r**5 + 1/1080*r**6 - r + 0*r**2 + 0 - 1/72*r**4. Let u(m) be the second derivative of t(m). Factor u(g).
(g - 1)*(g + 1)/3
Let u(q) be the first derivative of q**8/1176 + 2*q**7/735 + q**6/420 - q**2/2 - 4. Let b(c) be the second derivative of u(c). Determine y, given that b(y) = 0.
-1, 0
Let t be (4 - 1) + (1 - -1). Suppose -4*f = q + q + 2, q = -t*f - 13. Factor 5*p + p**4 - 5*p + 9*p**2 + q*p + 5*p**3 + 2.
(p + 1)**3*(p + 2)
Let s = 11 + -54/5. Let f(r) be the first derivative of 3/5*r**4 + 1/15*r**6 + 1 + 8/25*r**5 + 0*r + 8/15*r**3 + s*r**2. Factor f(o).
2*o*(o + 1)**4/5
What is z in -2 + 2*z**2 - 117*z + 117*z = 0?
-1, 1
Suppose y - 2 + 1 = 0. Suppose b + 3*b - 8 = 0. Factor -y - n**2 + 2*n + n**3 - 2*n + 3*n - b*n**2.
(n - 1)**3
Solve -4/7*k + 0 - 6/7*k**2 + 0*k**3 + 2/7*k**4 = 0 for k.
-1, 0, 2
Let o(w) = -w**3 - 6*w**2 + 7*w + 3. Let j be (14/8)/((-3)/12). Let u be o(j). Solve 7 - 25*d**5 + 24*d - 3*d**3 - 3 - 45*d**4 + 4*d**u + 41*d**2 = 0.
-1, -2/5, 1
Let c(u) be the first derivative of -u**3/5 + 18*u**2/5 - 108*u/5 + 13. Solve c(a) = 0.
6
Let 4*m**3 - m**4 - 5*m**3 + 12*m - 2*m**4 - 8*m**3 = 0. What is m?
-2, 0, 1
Factor -4*o + 100 + 4*o**2 - 14*o - 22*o.
4*(o - 5)**2
Let a be (-4)/10 + (-10)/(-24). Let t(d) be the third derivative of 0 + 2*d**2 - a*d**4 + 0*d - 2/15*d**3 + 1/150*d**5. Suppose t(o) = 0. What is o?
-1, 2
Let a(w) be the first derivative of -2*w**6/3 + 4*w**5/15 + 2*w**4 - 8*w**3/9 - 2*w**2 + 4*w/3 - 42. Suppose a(s) = 0. What is s?
-1, 1/3, 1
Suppose -5*f = -4*q - 5, f = 4*q - 1 + 2. Suppose -3*z + 2*z + 4 = q. Factor 0*d + 3/4*d**2 + 0 - 3/4*d**z + 0*d**3.
-3*d**2*(d - 1)*(d + 1)/4
Let m(u) = -6*u**3 + 4*u - 4. Let r(t) = t**3 - t + 1. Let d(a) = m(a) + 5*r(a). Let x(c) = -2*c**2 + 4*c. Let q(b) = 2*d(b) + x(b). Factor q(k).
-2*(k - 1)*(k + 1)**2
Let w(l) be the first derivative of l**6/4 - 6*l**5/5 + 9*l**4/4 - 2*l**3 + 3*l**2/4 + 1. Factor w(z).
3*z*(z - 1)**4/2
Let h(c) = 2*c**2 - c + 1. Let i be h(1). Let l = -8/5 + 2. What is o in 0*o + 2/5*o**i - l = 0?
-1, 1
Suppose 2*b + 520 = 522. Factor 1/4*n**3 + 0*n + 3/4*n**2 - b.
(n - 1)*(n + 2)**2/4
Let i(v) be the first derivative of -2*v**3/9 + 4*v**2/3 - 8*v/3 - 30. Factor i(o).
-2*(o - 2)**2/3
Let r(o) be the first derivative of 3/2*o**2 + o**3 + 0*o - 3. Find j, given that r(j) = 0.
-1, 0
Let y(t) be the second derivative of 7*t**6/15 + t**5/5 - 7*t**4/6 - 2*t**3/3 + 6*t. Find m such that y(m) = 0.
-1, -2/7, 0, 1
Let r(d) = -d**3 + 10*d**2 - 7*d - 7. Let j be r(9). Suppose -5*p - 10 = -4*k, p - 3*k + 2 + j = 0. What is s in s**p + 1/2 - 3/2*s = 0?
1/2, 1
Let r(m) = 10*m**2 + 7 + 3 + m**3 - 5. Let i be r(-10). Factor i*x**2 + 1 + 3*x + 0*x**2 - x - 4*x**2.
(x + 1)**2
Let b(x) be the second derivative of -x**7/63 + x**6/15 + x**5/15 - x**4/3 - x**3/9 + x**2 - x. Let b(z) = 0. What is z?
-1, 1, 3
Suppose r = 6*r. Let h(l) be the second derivative of 1/48*l**4 - 2*l - 1/24*l**3 + r + 0*l**2. Solve h(s) = 0 for s.
0, 1
Let r(y) be the first derivative of y**4/4 - 5*y**3/3 - y**2/2 + 7*y + 1. Let a be r(5). Factor 0*q**4 + q**3 - q**2 - q**4 + a*q**2 - q.
-q*(q - 1)**2*(q + 1)
Let a(o) be the third derivative of o**8/84 - 2*o**7/35 + o**6/30 + o**5/5 - o**4/3 - 38*o**2. Factor a(y).
4*y*(y - 2)*(y - 1)**2*(y + 1)
Factor -12 - 31*t**2 + 16*t**2 + 18*t**2.
3*(t - 2)*(t + 2)
Factor 4*l**4 - 4*l - 19*l**2 + 2*l + 2*l**5 + 15*l**2.
2*l*(l - 1)*(l + 1)**3
Let r = 20/9 + -17/9. Let d be 20/(-8)*24/(-20). Factor -1/3*b - 1/3*b**2 + r*b**d + 1/3.
(b - 1)**2*(b + 1)/3
Let l(o) be the second derivative of o**6/30 + o**5/40 - o**4/24 - 2*o. Factor l(g).
g**2*(g + 1)*(2*g - 1)/2
Let z be 1 + -1 + (-8)/(-24). Let p be ((-1)/(-4))/(3/16). Factor 1/3*j + 2*j**3 + z*j**5 - p*j**4 + 0 - 4/3*j**2.
j*(j - 1)**4/3
Let r = -293 + 3225/11. Solve 2/11*j + 0 + r*j**3 - 4/11*j**2 = 0.
0, 1
Determine k, given that -k**3 - 5*k + 5*k + 3*k**2 - 2*k = 0.
0, 1, 2
Suppose 5*w = 61 - 51. Suppose 0*n = -3*n. Factor n*j + 1/3 - 1/3*j**w.
-(j - 1)*(j + 1)/3
Let s = -784/5 + 157. Let -s*t - 2/5*t**2 + 0 - 1/5*t**3 = 0. Calculate t.
-1, 0
Let i be 64/78 - 0 - 126/819. Factor -2/9 + 2/3*j - 2/9*j**5 - 4/9*j**3 + i*j**4 - 4/9*j**2.
-2*(j - 1)**4*(j + 1)/9
Suppose 4 + 0 = 4*r + 2*h, 2*h = 4*r + 4. Let i be (2/(-9))/(5/(-10)). Factor -2/9*t**2 + r*t - i*t**3 + 0.
-2*t**2*(2*t + 1)/9
Let a(i) = -2*i**2 + 30*i - 62. Let o(y) = y**2 - y + 1. Suppose 0 = -0*g + 3*g - 3. Let s(t) = g*a(t) - 2*o(t). Factor s(c).
-4*(c - 4)**2
Let i(w) be the first derivative of w**6/6 + w**5/5 - w**4/4 - w**3/3 - 2. Factor i(t).
t**2*(t - 1)*(t + 1)**2
Suppose 2*c + 2*c - 12 = 0. Let k = 3 + c. Find p, given that 6*p - k*p**3 - 21*p**4 + 3*p**2 + 16*p**2 + 2*p**2 = 0.
-1, -2/7, 0, 1
Let r(s) be the second derivative of 0 - 1/10*s**3 - 3/5*s**2 + s + 1/20*s**4. Find g, given that r(g) = 0.
-1, 2
Let n = -6 - -17. Suppose -2*u = -4*i + u - n, -4*u = -i - 19. Find h, given that -i - 1/2*h + 1/2*h**3 + h**2 = 0.
-2, -1, 1
Suppose -5*r = -13*r. Suppose 4/7*f**3 + 2/7*f + 8/7*f**2 - 8/7*f**4 - 6/7*f**5 + r = 0. Calculate f.
-1, -1/3, 0, 1
Let r(q) = -100*q**3 - 208*q**2 + 76*q + 56. Let o(b) = 9*b**3 + 19*b**2 - 7*b - 5. Let j(t) = 32*o(t) + 3*r(t). Factor j(p).
-4*(p + 1)**2*(3*p - 2)
Factor 1/2*y - 1/2*y**4 + 1/2*y**5 + y**2 - y**3 - 1/2.
(y - 1)**3*(y + 1)**2/2
Suppose 0 = 16*x - 9*x - 2*x. Factor 2/3*f**3 - 8/9 + 14/9*f**2 + x*f.
2*(f + 1)*(f + 2)*(3*f - 2)/9
Let l be (-3 - 6/(-1))*1. Factor -6*n**3 + 15*n + 0 + 12 - 9*n**2 - 3*n + l*n**4.
3*(n - 2)**2*(n + 1)**2
Solve -2*n + 8/5*n**3 - 4/5*n**2 + 2/5*n**5 - 4/5 + 8/5*n**4 = 0.
-2, -1, 1
Suppose 0 = 4*y - 4*s - 3 - 13, 0 = 2*y + 2*s - 12. Let c(x) be the second derivative of 1/24*x**4 - 1/80*x**y - 1/24*x**3 - x + 0 + 0*x**2. Factor c(m).
-m*(m - 1)**2/4
Let l be (1/(-2))/(2/(-120)). Suppose 2 + 3*a**3 - 8*a**3 - 14*a + l*a**2 - 13*a**3 = 0. What is a?
1/3, 1
Solve 0*k**4 + k**4 - 12*k**3 + 0*k**4 - 2*k + 14*k**3 - 1 = 0 for k.
-1, 1
Let i(d) be the first derivative of d**5/30 + d**4/6 + 5*d - 4. Let b(r) be the first derivative of i(r). Determine v, given that b(v) = 0.
-3, 0
Suppose 2 = -r + 2. Let f(m) be the third derivative of 1/24*m**4 + r*m**3 + 0 + 0*m - 1/60*m**5 - 3*m**2. Suppose f(b) = 0. What is b?
0, 1
Let x(h) be the second derivative of h**3 + 0 + 3/4*h**4 + 0*h**5 + 0*h**2 - 5*h - 1/10*h**6. Solve x(o) = 0.
-1, 0, 2
Let c(t) be the third derivative of t**7/280 + 7*t**6/480 - t**5/240 - 7*t**4/96 - t**3/12 - 14*t**2. Suppose c(g) = 0. Calculate g.
-2, -1, -1/3, 1
Let i(y) = 6*y**2 - 3*y - 3. Let d(l) = -l**3 + 6*l**2 - 3*l - 2. Let o(r) = -3*d(r) + 2*i(r). Suppose o(n) = 0. What is n?
0, 1
Determine n so that 0 - 1/4*