2, -1, 1
Let z(r) be the first derivative of -2*r**5/5 - 2*r**4 - 4*r**3/3 + 4*r**2 + 6*r + 13. Suppose z(m) = 0. What is m?
-3, -1, 1
Let z(v) = 3*v**2 - 9*v - 2. Let w(u) = u**2 + 6*u - 7. Let m be w(-7). Let t = -4 + m. Let n(x) = -2*x**2 + 8*x + 2. Let s(r) = t*z(r) - 5*n(r). Factor s(h).
-2*(h + 1)**2
Let x be (-8)/6*15/(-2). Let p = -1 + 3. Solve 0*f**p - 3*f**5 - 2*f**2 - 3*f**3 - 6*f**3 - x*f**4 = 0 for f.
-2, -1, -1/3, 0
Solve 45*q**2 + 216 - 30*q**4 - 8*q + 17*q**2 + 32*q**3 - 224 = 0 for q.
-1, -1/3, 2/5, 2
Let y(o) be the second derivative of -1/36*o**4 - 1/90*o**6 + 0 + 0*o**2 + 0*o**3 - 1/30*o**5 + o. Find j, given that y(j) = 0.
-1, 0
Let d(z) be the third derivative of -z**8/3360 - z**7/672 + z**5/96 + z**4/48 + z**3/3 + 2*z**2. Let y(a) be the first derivative of d(a). Solve y(n) = 0.
-2, -1, -1/2, 1
Suppose 2*n - 27 = -o, -81 = -4*n - 5*o - 30. Solve -m**4 - 4*m**2 + 5*m**4 + 14*m**5 + 0*m**4 - n*m**3 = 0 for m.
-1, -2/7, 0, 1
Let x(t) be the second derivative of -1/3*t**3 + 2*t**2 + 0 - 2*t - 1/6*t**4. Solve x(q) = 0 for q.
-2, 1
Let n(y) be the second derivative of y**5/20 - y**4 + 8*y**3 - 32*y**2 + 4*y. Factor n(d).
(d - 4)**3
Solve -7*u**3 + u**3 - 20*u**2 + 2*u**3 = 0.
-5, 0
Let k be -1 - (1*-12 - -2). Factor 23*a**3 - 40*a**2 - a + k*a - 14*a**4 + 19*a**3 + 4*a**3.
-2*a*(a - 2)*(a - 1)*(7*a - 2)
Let x(l) be the first derivative of -l**3/9 - l**2/2 - 2*l/3 - 20. Factor x(c).
-(c + 1)*(c + 2)/3
Let s = 148 + -1626/11. What is x in 0*x + 2/11 - s*x**2 = 0?
-1, 1
Let s be ((-32)/(-12) - 3) + 2/2. Solve -4/3*p**3 + s*p + 2/3*p**5 + 4/9 + 4/9*p**4 - 8/9*p**2 = 0.
-1, -2/3, 1
Suppose q + 0*q - 4*k + 18 = 0, 3*q - 21 = -3*k. What is t in 20 - 300*t**3 + 337*t**q - 375*t**4 + 324*t - 67*t**2 + 61 = 0?
-3/5, 1
Let u(f) be the third derivative of -1/3*f**3 - 1/225*f**6 + 0 - 2*f**2 + 0*f - 1/60*f**4 - 1/60*f**5. Let g(l) be the first derivative of u(l). Factor g(c).
-2*(c + 1)*(4*c + 1)/5
Let d(z) be the first derivative of -4*z**6/105 + 4*z**5/105 - z**4/84 + z**2/2 - 3. Let n(v) be the second derivative of d(v). Factor n(w).
-2*w*(4*w - 1)**2/7
Let g(a) be the third derivative of 0*a - 1/120*a**6 + 1/210*a**7 + 0*a**3 - 1/60*a**5 - 2*a**2 + 1/24*a**4 + 0. Let g(l) = 0. What is l?
-1, 0, 1
Let k(d) = 2*d**2 + 3*d + 1. Let v be k(-2). Let -h**2 + 3*h**2 + 4*h + v*h**3 - h + 4*h**2 = 0. Calculate h.
-1, 0
Suppose -7*z = 3*z - 5*z. Let d(a) be the third derivative of -1/360*a**6 + 0*a - 1/36*a**4 + 1/60*a**5 + z + 0*a**3 + 4*a**2. Let d(o) = 0. What is o?
0, 1, 2
Let g = 30/13 + -137/65. Determine d so that -g*d + 2/5 - 2/5*d**2 + 1/5*d**3 = 0.
-1, 1, 2
Suppose -11 = 5*y + 4. Let v(q) = q**2 + 3*q + 3. Let j be v(y). Suppose -15*k**4 - 39*k**3 - 27*k**2 + j*k + 12 - 3 - 3 = 0. Calculate k.
-1, 2/5
Factor -2*p**3 + 341*p + 9006 + 72*p**2 - 5550 - 1205*p.
-2*(p - 12)**3
Factor 0*q + 8/7 - 2/7*q**2.
-2*(q - 2)*(q + 2)/7
Suppose 4/5*h**2 + 4/5*h - 1/5*h**3 + 0 - 1/5*h**4 = 0. What is h?
-2, -1, 0, 2
Let a(s) = -2*s**4 + 10*s**3 + 22*s**2 + 10*s + 8. Let n(h) = -h**4 + 10*h**3 + 21*h**2 + 11*h + 7. Let o(j) = -3*a(j) + 4*n(j). Let o(t) = 0. Calculate t.
-2, -1
Suppose -4*r = -0*r. Let o(b) be the third derivative of 0*b**3 - 1/60*b**6 + 0 + 1/12*b**4 + r*b**5 + b**2 + 0*b. Factor o(t).
-2*t*(t - 1)*(t + 1)
What is o in -7*o**3 + o**3 - 4*o**3 + 10*o**5 - 5*o**5 + 5*o = 0?
-1, 0, 1
Let n be (5 - (-52)/(-8))/(-45). Let o(p) be the second derivative of 4/5*p**2 + n*p**4 + 4/15*p**3 + 0 + p. Suppose o(x) = 0. What is x?
-2
Factor h**2 + 0 - 3/2*h**3 + 0*h + 0*h**4 + 1/2*h**5.
h**2*(h - 1)**2*(h + 2)/2
Let w(r) be the third derivative of 0*r + 0 - 4*r**2 - 1/144*r**4 - 1/18*r**3 + 1/360*r**5. Factor w(n).
(n - 2)*(n + 1)/6
Let c = 553/1082 - 6/541. Factor 0 + c*f - 9/4*f**2 - 1/2*f**3 + 9/4*f**4.
f*(f - 1)*(f + 1)*(9*f - 2)/4
What is w in 0 - 1/3*w - 1/3*w**4 - w**2 - w**3 = 0?
-1, 0
Let j(q) be the third derivative of q**5/210 + q**4/21 + q**3/7 - 13*q**2. What is f in j(f) = 0?
-3, -1
Suppose 8/5*b + 6/5*b**2 + 2/5 = 0. Calculate b.
-1, -1/3
Let x(h) be the first derivative of h**4/4 + 7*h**3/3 + 34. Factor x(t).
t**2*(t + 7)
Let b be 3/(-6) + (-108)/(-24). Determine a so that a**3 - 2 - 5/2*a**b + 15/2*a**2 + 2*a = 0.
-1, 2/5, 2
Solve 2/3*n + 0 - 2/3*n**2 = 0 for n.
0, 1
Let n = -1 + 7. Suppose -n*u = -4*u - 6. What is d in -1 - u*d**2 + 0*d**2 + 4*d**2 = 0?
-1, 1
Let g be 16/(-6)*(-3)/(-2). Let f be (-7 - g)*(-2)/12. Factor 0 - 1/4*x + f*x**2 - 1/4*x**3.
-x*(x - 1)**2/4
Let m(h) = -60*h**5 - 85*h**4 - 25*h + 25. Let x(j) = -5*j**5 - 7*j**4 - 2*j + 2. Let f(y) = -2*m(y) + 25*x(y). Factor f(s).
-5*s**4*(s + 1)
Let q(j) be the second derivative of 5*j**7/42 - 3*j**5/4 + 5*j**4/6 + 55*j. Solve q(g) = 0 for g.
-2, 0, 1
Suppose -2*x - q = 6 - 9, 4*q - 12 = 5*x. Factor 0*z**2 - 1/2*z**4 + 0 + x*z - 3/4*z**5 + 1/4*z**3.
-z**3*(z + 1)*(3*z - 1)/4
Factor -14*u**2 - u**3 - 3*u + 3*u + 15*u**2.
-u**2*(u - 1)
Let m(t) be the second derivative of 0*t**3 + 0*t**5 + 0 - t - 1/90*t**6 + 0*t**2 + 1/36*t**4. Solve m(v) = 0 for v.
-1, 0, 1
Let x = -7 + 8. Factor -v**2 - 4 - x + 0*v**2 + 1 + 4*v.
-(v - 2)**2
Let f(o) be the third derivative of 0*o + 0 + 0*o**3 + 0*o**5 + 3*o**2 + 1/12*o**4 - 1/60*o**6. Factor f(g).
-2*g*(g - 1)*(g + 1)
Let x(t) = t - 1. Let u be x(1). Let 84/5*v**4 + 8/5*v**3 - 18*v**5 - 16/5*v**2 + 0 + u*v = 0. Calculate v.
-2/5, 0, 2/3
Let m(z) be the third derivative of z**5/150 + z**4/60 + 7*z**2. Suppose m(v) = 0. What is v?
-1, 0
Let k(p) be the third derivative of p**8/84 - 2*p**7/35 - 11*p**6/15 - 38*p**5/15 - 9*p**4/2 - 14*p**3/3 - 4*p**2 - p. Factor k(t).
4*(t - 7)*(t + 1)**4
Let p be (((-6)/5)/(-3))/(16/32). Suppose 36/5 + 24/5*c + p*c**2 = 0. Calculate c.
-3
Let o be (95/(-114))/((-15)/9). Factor -1/2*n**3 - 3/2 - o*n**2 + 5/2*n.
-(n - 1)**2*(n + 3)/2
Let h = 191/18 + -21/2. Let x(b) be the first derivative of 8/9*b**3 + 1/2*b**4 - h*b**6 - 4/3*b**2 - 4/15*b**5 + 3 + 0*b. Factor x(q).
-2*q*(q - 1)**2*(q + 2)**2/3
Let y(n) be the third derivative of -n**8/462 - n**7/231 + n**6/60 + 23*n**5/330 + 13*n**4/132 + 2*n**3/33 + 10*n**2. Determine f, given that y(f) = 0.
-1, -1/4, 2
Let p be (-6)/16*1/(-3). Let o(u) be the first derivative of -2 + 1/4*u**3 + 0*u + p*u**2. Factor o(z).
z*(3*z + 1)/4
Let s(f) = -7*f**2 + 2*f - 6. Let x(w) = -8*w**2 + 2*w - 7. Let i(l) = 7*s(l) - 6*x(l). What is k in i(k) = 0?
0, 2
Let y(h) be the first derivative of h**3/18 + h**2/6 - h/2 - 4. Let y(n) = 0. Calculate n.
-3, 1
Let g(s) = 4*s**5 + 4*s**4 - 6*s**3 - 2*s**2 + 6*s. Let x(z) = -z**5 - z**4 - z. Let k(c) = -2*g(c) - 4*x(c). Determine h so that k(h) = 0.
-2, -1, 0, 1
Suppose k + 10 = -5*b - 0*b, 5*b - 5 = -4*k. Let a be 7/k + 2 + -3. Factor 0 + 4/5*j**2 + a*j.
2*j*(2*j + 1)/5
Let m(q) = 4*q**2 - 1. Let p be m(-1). Let t(a) be the second derivative of 0*a**2 - 1/27*a**p + 0 + 1/54*a**4 + 3*a. Determine y, given that t(y) = 0.
0, 1
Factor 1/3*x**4 - 1/3*x + 1/3*x**3 + 2/3 - x**2.
(x - 1)**2*(x + 1)*(x + 2)/3
Let 6/5*s**2 + 0 - 4/5*s - 2/5*s**3 = 0. Calculate s.
0, 1, 2
Let v = -133/2 + 67. Factor 1/2*l**2 + 0 + v*l.
l*(l + 1)/2
Let v(t) be the third derivative of 0 + t**2 + 1/315*t**7 + 0*t + 0*t**3 + 1/90*t**6 - 1/90*t**5 - 1/18*t**4. Determine o so that v(o) = 0.
-2, -1, 0, 1
Let n(m) be the second derivative of m**7/2520 - m**6/240 + m**4/12 + 6*m. Let f(d) be the third derivative of n(d). Factor f(q).
q*(q - 3)
Factor -4*k + 5 + 4*k**3 - 12*k**2 + 10 - 3 + 0.
4*(k - 3)*(k - 1)*(k + 1)
Suppose -16 = 2*z - 5*m, 3*z = 2*m - 2 - 0. Factor 1 + w**2 - 3*w**2 + z*w + 3*w**2.
(w + 1)**2
Let f(k) = 6*k**4 + 4*k**3 - 8*k**2 - 4*k + 10. Let l(g) = -g**4 + g**2 - 1. Suppose -3*o = -4*r + 2*o + 19, 6 = -2*o. Let b(c) = r*f(c) + 8*l(c). Factor b(p).
-2*(p - 1)**3*(p + 1)
Let z = 9 + -3. Factor 3*w**3 - z*w**2 + 3*w + 0*w**3 + 6 - 6*w**3.
-3*(w - 1)*(w + 1)*(w + 2)
Factor 3*k**5 + 0*k**3 + 4*k**4 - k**5 - 3*k**3 + 5*k**3.
2*k**3*(k + 1)**2
Let l(b) be the second derivative of b**5/80 + b**4/48 - 6*b. Solve l(g) = 0.
-1, 0
Let d(c) be the first derivative of 2*c**5/5 - c**4/8 - 2*c**3/3 + c**2/4 + 36. Solve d(z) = 0.
-1, 0, 1/4, 1
Let v = -85 + 89. Determine z, given that 4/3*z + 2/3*z**v - 2*z**5 - 6*z**2 + 0 + 6*z**3 = 0.
-2, 0, 1/3, 1
Let s be 539/(-28) 