y + 1)**2*(9*y - 2)
Suppose -3*l + 0*x + 4*x = 4, 5*l - 5*x = -5. Let h(q) be the second derivative of 1/3*q**3 - 1/2*q**2 + 2*q + l - 1/12*q**4. Factor h(n).
-(n - 1)**2
Let a = -105 - -107. Let h(z) be the third derivative of 0*z**3 + 0 + 0*z**4 - 1/60*z**6 + 0*z**5 + 1/105*z**7 - z**a + 0*z. Factor h(y).
2*y**3*(y - 1)
Let k = 268/695 - -2/139. Let i = -2/417 - -2512/2085. Factor 0*p**2 + 4/5*p**3 + k*p**5 + i*p**4 + 0 + 0*p.
2*p**3*(p + 1)*(p + 2)/5
Let w(y) be the first derivative of -4 + 0*y - 4/21*y**3 + 4/35*y**5 + 1/21*y**6 + 0*y**4 - 1/7*y**2. Factor w(v).
2*v*(v - 1)*(v + 1)**3/7
Let j(v) be the second derivative of v**6/210 - v**5/70 - v**4/21 + v**3/21 + 3*v**2/14 - 6*v. Solve j(k) = 0.
-1, 1, 3
Let j(z) = -z**2 + 8*z - 7. Let w be j(6). Suppose -1 = s + r + 2*r, 0 = -4*s + w*r + 13. What is q in -1/2*q + 0 + 1/4*q**s + 1/4*q**3 = 0?
-2, 0, 1
Let i = -4/91 + 37/546. Let s(n) be the second derivative of 1/7*n**2 - i*n**4 + 0 + 0*n**3 + 2*n. Suppose s(b) = 0. What is b?
-1, 1
Let s(v) be the third derivative of -1/15*v**5 + 0*v + 0*v**3 - 7/60*v**6 + 2/105*v**7 + 0*v**4 - 7*v**2 + 0 + 1/24*v**8. Solve s(u) = 0.
-1, -2/7, 0, 1
Let h be 2/4 - 4/8. Let s(u) be the second derivative of 1/12*u**3 + 0 + 5/24*u**4 - 2*u + 1/10*u**5 + h*u**2. Suppose s(i) = 0. What is i?
-1, -1/4, 0
Let w be 92/(-20) - (-10)/2. Factor -3/5*u + w*u**2 + 0.
u*(2*u - 3)/5
Let w(c) be the second derivative of -3*c**5/10 - 15*c**4/8 - 2*c**3 + 9*c**2/4 - 2*c. Suppose w(t) = 0. What is t?
-3, -1, 1/4
Factor -1/3 - 7/6*i - 1/6*i**4 - 3/2*i**2 - 5/6*i**3.
-(i + 1)**3*(i + 2)/6
Let t(c) be the second derivative of 7*c**5/30 + 11*c**4/36 + c**3/9 + 36*c. What is f in t(f) = 0?
-1/2, -2/7, 0
Suppose -28 = -3*b + 101. Let -h**4 - h**3 + 43*h**2 - b*h**2 = 0. What is h?
-1, 0
Let l(k) be the second derivative of -k**6/60 - k**5/4 - k**4 + 5*k**3/6 + 25*k**2/4 + 30*k. Factor l(x).
-(x - 1)*(x + 1)*(x + 5)**2/2
Determine a so that 25/4*a**4 - 45/2 + 165/4*a**3 + 305/4*a**2 + 75/4*a = 0.
-3, -1, 2/5
Let o = 3117/13 - 240. Let c = o - -51/52. Suppose 3/4*k**2 + 1/4*k**3 + 1/4 + c*k = 0. Calculate k.
-1
Let t(m) = 0 - m - 2*m**4 + 4*m - m**3 + 0. Let y(b) = 5*b**4 + 2*b**3 - 7*b. Let z(j) = 7*t(j) + 3*y(j). Suppose z(x) = 0. Calculate x.
0, 1
Let l = 1 + 4. Solve 0*z**2 + l*z**2 - 2*z**2 = 0.
0
Suppose -31 - 4*t**2 - 9 - 247*t + 219*t = 0. Calculate t.
-5, -2
Let b = 8 + -5. Factor -1/4*r + 0 + 1/2*r**4 - 1/2*r**2 + 1/4*r**5 + 0*r**b.
r*(r - 1)*(r + 1)**3/4
Let m(u) be the third derivative of 0 - 1/1176*u**8 + 2/735*u**7 - 1/105*u**5 + 0*u + 0*u**3 + 1/84*u**4 + 0*u**6 - 3*u**2. Factor m(r).
-2*r*(r - 1)**3*(r + 1)/7
Let m(v) be the first derivative of 2*v**6/27 - v**4/9 - 1. Suppose m(n) = 0. What is n?
-1, 0, 1
Let t(z) = 2*z + 5. Let m be t(-5). Let q = -2 - m. Factor v**2 - 2*v**2 + 0*v - 2*v**q + 2*v**2 + 2*v - v**4.
-v*(v - 1)*(v + 1)*(v + 2)
Let x = -15/4 - -137/28. Suppose 0 + 2/7*p**5 - 8/7*p**4 + 2/7*p - x*p**2 + 12/7*p**3 = 0. Calculate p.
0, 1
Let b(f) = f**5 - 4*f**4 - f**3 + f**2 - 3*f - 3. Let y(s) = s**4 + s + 1. Let d be 6/(-8) + 9/(-36). Let g(i) = d*b(i) - 3*y(i). Solve g(c) = 0.
-1, 0, 1
Let q(d) be the second derivative of -d**4/48 - 7*d**3/12 + 15*d**2/8 + 65*d. Factor q(l).
-(l - 1)*(l + 15)/4
Let s(y) be the third derivative of -y**5/6 - y**4/36 - 19*y**2. Factor s(p).
-2*p*(15*p + 1)/3
Let o(d) be the second derivative of -3*d**5/80 - d**4/4 + d**3/8 + 3*d**2/2 + 2*d + 7. What is v in o(v) = 0?
-4, -1, 1
Let v = -47 + 50. What is b in -3*b**2 + 4/3*b**v + 2*b - 1/3 = 0?
1/4, 1
Suppose 5*s - 6 = 4*s. Let j(a) = -a**3 + 3*a**2 + 2. Let d(g) = 6*g**3 - 18*g**2 - g - 13. Let t(r) = s*d(r) + 39*j(r). Suppose t(f) = 0. Calculate f.
0, 1, 2
Let s = 21 - 18. Suppose 11*g**3 - s*g**2 - 6*g**3 + 3*g**4 - 4*g**5 + 0*g - g = 0. What is g?
-1, -1/4, 0, 1
Let m(k) be the third derivative of k**8/336 - k**7/105 - 7*k**6/120 - k**5/15 - 9*k**2. Factor m(y).
y**2*(y - 4)*(y + 1)**2
Let n(q) = -3*q**4 + 9*q**3 - 8*q**2 - 9*q + 11. Let t(r) = -3*r**4 + 9*r**3 - 9*r**2 - 9*r + 12. Let o(y) = 6*n(y) - 5*t(y). What is l in o(l) = 0?
-1, 1, 2
Let r(p) be the first derivative of p**6/15 - 2*p**5/5 + 5*p**4/6 - 2*p**3/3 - 4*p + 1. Let h(f) be the first derivative of r(f). Factor h(q).
2*q*(q - 2)*(q - 1)**2
Let h(x) be the first derivative of -x**6/15 + 2*x**5/25 + x**4/5 - 11. Factor h(n).
-2*n**3*(n - 2)*(n + 1)/5
Suppose -7*s = -0*s - 14. Factor -2/7*b - 4/7 + 2/7*b**s.
2*(b - 2)*(b + 1)/7
Let k(g) be the third derivative of -g**7/420 - g**6/180 + g**3/2 - g**2. Let i(o) be the first derivative of k(o). What is q in i(q) = 0?
-1, 0
Suppose 5*b - 2*y = 16, 3*b = 4*b - 4*y - 14. Factor 2*u - 3*u**2 + b*u**3 - 4*u**2 + u**2 + 2*u**2.
2*u*(u - 1)**2
Let x be ((-3)/(-6))/(3/(-720)). Let h = x - -842/7. Let h*p**3 + 2/7*p**2 - 2/7*p - 2/7 = 0. Calculate p.
-1, 1
Factor -3*t**3 + 7*t**5 + 4*t**3 - 8*t**5.
-t**3*(t - 1)*(t + 1)
Suppose 3*k - 9 + 0 = 0. Solve -2 - 2*l**k + 2*l + 2 = 0.
-1, 0, 1
Suppose 3*y + 5 = -19. Let h(v) = -v**3 - 7*v**2 + 9*v + 8. Let c be h(y). Determine m so that -1/6*m**5 + 1/6*m + 0 + 1/3*m**2 + c*m**3 - 1/3*m**4 = 0.
-1, 0, 1
Let t = -27 - -137/5. Solve -2/5*p**3 + 2/5*p**2 + 0 - t*p**4 + 2/5*p = 0.
-1, 0, 1
Let c(y) be the first derivative of 0*y**4 - 1 - 4/5*y**5 + 0*y**3 + 0*y**2 + 0*y. Factor c(d).
-4*d**4
Let o = 866 - 863. Factor 0 - 2/3*u**o - 4/3*u**2 - 2/3*u.
-2*u*(u + 1)**2/3
Let j(d) = -d**4 + d**2 + d - 1. Let q(r) = -12*r**5 + 4*r**4 - 2*r**2 + 30*r - 20. Suppose -186 = -6*n + 30. Let m(k) = n*j(k) - 2*q(k). What is l in m(l) = 0?
-1, 1/3, 1/2, 1
Let i(r) = -r**4 - r**3 + r**2 - r. Let z(x) = -4*x**5 - 10*x**4 + 2*x**3 + 14*x**2 - 10*x - 4. Let t(h) = -6*i(h) + z(h). Let t(y) = 0. What is y?
-1, 1
Suppose 2/3*c - 2/3*c**3 - 2/3*c**2 + 2/3 = 0. What is c?
-1, 1
Let s(v) be the third derivative of v**5/10 - v**4/8 - v**2. Factor s(a).
3*a*(2*a - 1)
Let l(a) be the first derivative of a**4/2 - 32*a**3/3 + 31*a**2 - 46*a - 4. Let h(b) = -b**2 + b - 1. Let m(s) = -28*h(s) + 2*l(s). Let m(z) = 0. What is z?
1, 4
Suppose -15 = 3*i, -2*n + 10 = -i + 1. Let 2/9*l**5 + 2/9*l**n + 0*l + 0 + 2/3*l**4 + 2/3*l**3 = 0. Calculate l.
-1, 0
What is s in -3/5*s**5 + 4/5*s**3 + 0 - 4/5*s**4 + 0*s**2 + 0*s = 0?
-2, 0, 2/3
Let u(n) be the first derivative of -5*n**4/4 + 4*n**3/9 + 3*n**2/2 + 2*n/3 + 5. Find m, given that u(m) = 0.
-2/5, -1/3, 1
Let c = 1210/7 - 172. Factor 0 + c*s + 2/7*s**2.
2*s*(s + 3)/7
Let v(p) be the second derivative of 0*p**2 + 1/21*p**7 + 0*p**6 + 0*p**4 + 0 - 2*p - 1/5*p**5 + 1/3*p**3. Solve v(d) = 0 for d.
-1, 0, 1
Let l(n) be the second derivative of 1/12*n**3 + 1/4*n**4 + n - 1/15*n**6 + 0 - 1/10*n**5 - 1/2*n**2 + 1/28*n**7. Determine y so that l(y) = 0.
-1, -2/3, 1
Let t be (-4 + 3)*4/(-10). Factor 2/5*k**3 - 2/5*k - 2/5*k**2 + t.
2*(k - 1)**2*(k + 1)/5
Determine m, given that 4*m + 2/3*m**2 - 14/3 = 0.
-7, 1
Suppose 2*p - 6*p - 5*s - 17 = 0, 0 = 3*s + 15. Factor -v**3 - 2*v + 3*v**3 - v**4 - 4*v**p + 5*v**4.
2*v*(v - 1)*(v + 1)*(2*v + 1)
Let z(k) = 9*k**3 + 4*k**2 + 5*k - 2. Let w = -6 - -6. Let i(c) = 0*c + 2 - 5*c**2 - 8*c**3 + w*c - 4*c. Let s(y) = 4*i(y) + 3*z(y). Factor s(r).
-(r + 1)**2*(5*r - 2)
Let b(s) = 2 + 1 + s + 4 + 0. Let m be b(-5). Factor -t + 7/2*t**3 + 5/2*t**m + 0.
t*(t + 1)*(7*t - 2)/2
What is s in 1/9*s**3 + 2/9*s**5 + 0 + 0*s**2 + 1/3*s**4 + 0*s = 0?
-1, -1/2, 0
Let y(c) = c**3 - 5*c**2 + 2. Let i = -8 + 13. Let l be y(i). Factor 4*k**2 - 2*k**5 + 0 - 8*k**4 + 2*k**4 + l - 4*k**3 + 6*k.
-2*(k - 1)*(k + 1)**4
Let h(u) be the first derivative of -1/24*u**6 - 1/20*u**5 - 4 - 1/8*u**2 - 1/4*u + 1/8*u**4 + 1/6*u**3. Factor h(x).
-(x - 1)**2*(x + 1)**3/4
Suppose 5*n + 4*u + 6 = 0, -8*u + 3*u - 10 = 5*n. Find q such that q**4 + 2*q**3 - n*q**3 + q**5 = 0.
-1, 0
Let n be (-2)/(-6)*-1 + (-20)/(-6). Determine p, given that 0*p + 0 + 1/4*p**n - 1/4*p**2 = 0.
0, 1
Let r(a) be the third derivative of a**8/6720 + a**7/5040 - a**6/1440 + a**4/8 - a**2. Let l(o) be the second derivative of r(o). Factor l(h).
h*(h + 1)*(2*h - 1)/2
Let b = 1 - 1. Suppose 28 = -a + 8*a. Factor 1/2*j**2 - 1/2*j**a + b*j**3 + 0*j + 0.
-j**2*(j - 1)*(j + 1)/2
Factor -10*q**4 + 5*q**5 - q**5 + 14*q**3 - 6*q**2 + 0*q**3 - 2*q**5.
2*q**2*(q - 3)*