p**2 - 2*p - 3. Let v be j(3). Let d(w) = w**2 + 10*w + 13. Let y be d(v). Solve 4*l**4 - 11*l**3 + 4*l**2 + l**2 + 0*l**y + 2*l = 0.
-1/4, 0, 1, 2
Factor 12/7*r**2 + 0*r + 4/7*r**3 - 16/7.
4*(r - 1)*(r + 2)**2/7
Let r(y) = -9*y**3 - 156*y**2 - 2023*y - 8793. Let a(m) = 10*m**3 + 156*m**2 + 2022*m + 8794. Let g(x) = 5*a(x) + 6*r(x). Factor g(w).
-4*(w + 13)**3
Let m(t) be the first derivative of 3*t**6/40 - t**5/5 + t**4/8 - 2*t**2 - 1. Let l(z) be the second derivative of m(z). Let l(v) = 0. What is v?
0, 1/3, 1
Let s = -74/9 - -376/45. Let m(h) be the second derivative of 0 + 0*h**2 - 16/25*h**5 - 7/15*h**7 + s*h**4 - 4*h + 0*h**3 + 77/75*h**6. Factor m(t).
-2*t**2*(t - 1)*(7*t - 2)**2/5
Let s(u) = 4*u**4 + 20*u**3 + 4*u**2 - 64*u - 60. Let d(b) = 4*b**4 + 21*b**3 + 5*b**2 - 64*b - 59. Let f(q) = -4*d(q) + 5*s(q). Factor f(c).
4*(c - 2)*(c + 2)**3
Let b = -1 - -3. Suppose -2 + w**2 - b*w**2 + 0*w + 3*w + 0 = 0. Calculate w.
1, 2
Let t be (-3)/(-5) - ((-188)/20 + 6). Let -4/3*z**3 + 0 + 2/3*z**5 + 0*z**2 + 0*z**t + 2/3*z = 0. Calculate z.
-1, 0, 1
Let f(k) be the second derivative of k**6/135 + 2*k**5/45 + 5*k**4/54 + 2*k**3/27 - 19*k. Factor f(i).
2*i*(i + 1)**2*(i + 2)/9
Suppose 0 = -t + 1 + 10. Suppose 2*k - 3*g - t = 0, k - 5*k = 2*g - 30. Factor 0*d + k*d**2 + 3*d - 4*d**2.
3*d*(d + 1)
Let l(b) = -2*b**5 + 4*b**3 - 6*b**2 - 2*b - 6. Let t(q) = -2*q**5 - q**4 + 5*q**3 - 6*q**2 - 3*q - 7. Let c(p) = -7*l(p) + 6*t(p). Factor c(m).
2*m*(m - 2)*(m - 1)**2*(m + 1)
Suppose 0 = -4*v - 3 + 11. Let x(z) be the second derivative of 0*z**3 + 0*z**v + 0*z**5 - 2*z + 0 + 1/15*z**6 - 1/6*z**4. Find m, given that x(m) = 0.
-1, 0, 1
Suppose 3*z = -6*x + x + 37, -3*x = 4*z - 31. Let w = x + -5. Find s such that 1/2*s**3 + w*s - 1/2*s**2 - 1/2*s**5 + 1/2*s**4 + 0 = 0.
-1, 0, 1
Factor 0*z**4 - 8*z**4 + 10*z**2 + z**4 - 4*z**3 + 4*z - 3*z**4.
-2*z*(z - 1)*(z + 1)*(5*z + 2)
Let f(h) = -4*h**4 + 4*h**3 - 3*h**2 + h + 1. Suppose 2*l + 2 = l. Let t(w) = -w**4 - w**3 - w**2 + w + 1. Let y(j) = l*f(j) + 2*t(j). Factor y(p).
2*p**2*(p - 1)*(3*p - 2)
Let d(u) be the first derivative of u**3/12 - 7. Factor d(n).
n**2/4
Let v = -4 - -40. Suppose 0 = -4*d + a - 5*a + v, 0 = 4*d - 5*a + 9. Factor d*k**2 + 2*k**3 + k**3 + 2*k**2.
3*k**2*(k + 2)
Let -c**4 - 10/7 - 33/7*c**3 + 33/7*c + 17/7*c**2 = 0. Calculate c.
-5, -1, 2/7, 1
Let m(x) be the first derivative of -2*x + 5/3*x**3 + 3/2*x**2 + 3. Find h such that m(h) = 0.
-1, 2/5
Suppose 4*d - f = -9, -4*d + 3*f = 8*f + 3. Let p be (-15)/(-9) - d/6. What is k in 0 + 0*k - 10/3*k**3 - 2*k**4 - 4/3*k**p = 0?
-1, -2/3, 0
Let v be (-2)/11 - (-46)/11. Solve 2*s**5 + 3*s**3 + 0*s**2 - 3*s**v - 4*s**2 + 7*s**4 - 5*s**3 = 0 for s.
-2, -1, 0, 1
Suppose x + 4*x - 25 = 0. Suppose 4*o - x*a = -a + 4, -4*a = -o - 8. Factor b**2 + 1/3*b**o - b**3 - 1/3*b + 0.
b*(b - 1)**3/3
Let u(g) be the second derivative of g**6/135 + 11*g**5/90 + g**4/2 + 25*g**3/27 + 8*g**2/9 + 14*g. Factor u(s).
2*(s + 1)**3*(s + 8)/9
Let n = -737/3 + 246. Suppose n*c**3 + 0 + 1/3*c**2 + 0*c = 0. Calculate c.
-1, 0
Let o(z) be the second derivative of -1/12*z**3 + 0*z**2 + 0 - 2*z - 1/16*z**4 - 1/80*z**5. Factor o(i).
-i*(i + 1)*(i + 2)/4
Suppose 302 - 62 = 60*q. Solve -2/9*m**q + 4/9*m**2 + 0*m**3 - 2/9 + 0*m = 0.
-1, 1
Let t = -42 + 42. Let x(i) be the first derivative of t*i - 2 + 0*i**2 - 1/6*i**3 - 1/4*i**4 - 1/10*i**5. Find v, given that x(v) = 0.
-1, 0
Factor 9/4*d + 0*d**2 - 3/2 - 3/4*d**3.
-3*(d - 1)**2*(d + 2)/4
Let u(a) be the first derivative of 3*a**5/20 - 3*a**4/8 + a**3/4 - 18. Factor u(m).
3*m**2*(m - 1)**2/4
Let q(x) be the second derivative of 3*x**5/100 - x**4/10 - 13*x**3/10 - 3*x**2 - 22*x. Let q(b) = 0. Calculate b.
-2, -1, 5
Let o(v) be the first derivative of -8/5*v**4 + 0*v**5 - 4/5*v + 7/5*v**2 + 3 + 3/5*v**6 + 4/15*v**3. Find p such that o(p) = 0.
-1, 1/3, 2/3, 1
Suppose 5 = 4*g + 1. Let r(w) = -w**3 - w**2. Let j(d) = -d**2 + 5*d**2 + 6*d**3 + 2*d**2. Let v(s) = g*j(s) + 4*r(s). Factor v(k).
2*k**2*(k + 1)
Let 90/11*w**3 + 0*w - 24/11*w**4 + 0 + 2/11*w**5 - 100/11*w**2 = 0. What is w?
0, 2, 5
Let f be (5 - 0) + 3 + (-9 - -3). Factor 4/5*c + 2/5*c**f + 2/5.
2*(c + 1)**2/5
Solve -12*c**3 - 12 - 2*c**4 + 2*c**2 - 10*c**2 + 2*c**5 + 4*c**4 + 2*c**4 + 26*c = 0.
-3, -2, 1
Let s(a) be the first derivative of -1/90*a**5 + a + 1/27*a**4 - 1/27*a**3 - 1 + 0*a**2. Let g(i) be the first derivative of s(i). Let g(t) = 0. What is t?
0, 1
Let h(y) be the third derivative of y**5/210 + y**4/84 + 5*y**2. Determine k so that h(k) = 0.
-1, 0
Let g be 24/16 + 6/(-4). Suppose w**2 + g*w**2 - 2*w**2 + 3*w**2 - 2*w**3 = 0. Calculate w.
0, 1
Let h(y) be the second derivative of y**7/189 + y**6/27 + y**5/10 + 7*y**4/54 + 2*y**3/27 + 24*y. Suppose h(a) = 0. What is a?
-2, -1, 0
Let p = -568/5 + 114. Suppose -2/5*c**4 + 4/5*c - 4/5*c**3 + 0*c**2 + p = 0. What is c?
-1, 1
Let u = -10 + 15. Suppose 0 = -u*g + 2 + 13. Let 0*y + 0 - 11/2*y**g + 8*y**4 + y**2 - 7/2*y**5 = 0. Calculate y.
0, 2/7, 1
Let n be 3/2 - (-1)/2. Let h(z) be the first derivative of -2/7*z**3 + 0*z - 2/7*z**2 - n. Factor h(b).
-2*b*(3*b + 2)/7
Let y be 3*((-4)/(-6))/1. Solve -y - 12*c**2 - 3*c + 10*c**2 + 1 = 0.
-1, -1/2
Factor 32/17*t**2 + 0 + 128/17*t + 22/17*t**4 - 72/17*t**3 - 2/17*t**5.
-2*t*(t - 4)**3*(t + 1)/17
Suppose -9*k = -11*k - 2. Let w be k/(2/(-6)) - 3. Factor 0*j - 8/7*j**2 + 6/7*j**4 + 2/7*j**5 + 0*j**3 + w.
2*j**2*(j - 1)*(j + 2)**2/7
Factor -13*r**2 + 0*r**2 - 7*r**2 + 2*r**3 - 7*r**3 - 15*r.
-5*r*(r + 1)*(r + 3)
Let d(s) be the second derivative of -s**5/5 + s**4 - 8*s**2 + 8*s. Solve d(m) = 0.
-1, 2
Let t be (-27)/36 + (-12)/(-2). Determine r so that -3*r**2 - 21/2*r**3 + 3/2 + t*r**5 + 3/2*r**4 + 21/4*r = 0.
-1, -2/7, 1
Suppose 0 = 3*g - 7*g + 3*c + 4, 5*g - 5 = 2*c. Let n = g + 4. Solve 0 - 42/5*j**n - 8/5*j - 24/5*j**2 + 6*j**3 + 44/5*j**4 = 0.
-2/3, -2/7, 0, 1
Let t be (-4)/(-1) + 2 + -4. Let s(b) be the third derivative of 0 + 0*b**5 + 1/630*b**7 + 1/180*b**6 - 1/18*b**3 + 0*b - 1/36*b**4 + t*b**2. Factor s(w).
(w - 1)*(w + 1)**3/3
Let r(h) = -h**3 - h + 1. Let z(f) = 7*f**3 + 3*f**2 + 9*f - 1. Let w(a) = 6*r(a) + z(a). Let p(x) be the first derivative of w(x). Factor p(v).
3*(v + 1)**2
Let l(f) = f - 4. Let r be l(3). Let x = -1 - r. Factor x - 2/5*u**2 - 2/5*u.
-2*u*(u + 1)/5
Let c(b) be the second derivative of 0 + 4/15*b**6 - 1/2*b**5 + 0*b**3 + 3*b + 0*b**2 + 1/6*b**4. Solve c(l) = 0 for l.
0, 1/4, 1
Determine v so that -2*v**2 + v + 3*v**2 - 2*v - 2*v**2 = 0.
-1, 0
Let r(v) = 3*v**3 + 2*v**2 - 5*v - 2. Let p(o) = -7*o**3 - 4*o**2 + 11*o + 5. Let x(i) = -2*p(i) - 5*r(i). Solve x(g) = 0.
-3, 0, 1
Factor -3*v**2 - v**2 + 5*v**2 + 3 + 3*v - 1.
(v + 1)*(v + 2)
Let m(v) be the second derivative of 0 - 1/24*v**4 + 1/4*v**3 - 1/2*v**2 + 2*v. Factor m(c).
-(c - 2)*(c - 1)/2
Let c = -20877/146 + 143. Let i = 577/1022 + c. Factor i*k + 2/7*k**2 + 2/7.
2*(k + 1)**2/7
Let s(p) = -p**3 + 5*p**2 - 3*p + 2. Let h be s(4). Factor -3*f**2 - 2*f**2 - f**4 + 7*f**2 + 7*f**3 - h*f**3.
-f**2*(f - 2)*(f + 1)
Let g(b) be the third derivative of b**8/1680 + b**7/150 + 19*b**6/600 + b**5/12 + 2*b**4/15 + 2*b**3/15 - 16*b**2. Factor g(o).
(o + 1)**3*(o + 2)**2/5
Let n(v) be the first derivative of v**3/6 - v**2 + 2*v - 6. Let n(x) = 0. What is x?
2
Let r be (-2)/(-2)*(-14)/(-21). Let k(w) be the first derivative of r*w**3 + 0*w**2 + 0*w - 1/4*w**4 - 1. Factor k(x).
-x**2*(x - 2)
Suppose 6 = w + 2*w. Let k(f) = -f**4 + f**3 - f. Let x(u) = 5*u**4 - 9*u**3 + 3*u**2 + 5*u - 2. Let q(a) = w*k(a) + x(a). Factor q(h).
(h - 1)**3*(3*h + 2)
Let z(j) be the third derivative of -j**5/120 - 7*j**4/24 - 49*j**3/12 + 3*j**2. Solve z(l) = 0.
-7
Let y = 1775/3094 - 1/442. Factor -y*t**4 + 2/7 - 6/7*t**2 + 10/7*t**3 - 2/7*t.
-2*(t - 1)**3*(2*t + 1)/7
Let k = -1273/2 - -649. Let v = -121/10 + k. Factor -4/5*z**3 + 4/5*z + 2/5 - v*z**2.
-2*(z - 1)*(z + 1)*(2*z + 1)/5
Let q(d) be the first derivative of d**4/2 + 4*d**3 + 12*d**2 + 16*d + 20. Find t such that q(t) = 0.
-2
Factor 3/7*d**5 + 6/7*d**2 + 0 + 0*d**3 - 6/7*d**4 - 3/7*d.
3*d*(d - 1)**3*(d + 1)/7
What is q in -14/9*q**4 - 6 + 4*q**2 + 2/9*q**5 + 20/9*q**3 - 6*q = 0?
-1, 3
Factor 0*o**3 + 0*o - 3*o + 0*o + 4*o**2 - o**3.
-o*(o - 3)*(o - 1)
Let a(r)