 = c**4 - c**3 + c**2 - c - 1. Let a(f) = -3*f**4 - 6*f**3 + 9*f**2 + 6. Let u(h) = -a(h) - 6*l(h). Suppose u(d) = 0. What is d?
0, 1, 2
Let t(r) be the second derivative of -1/42*r**4 + 0*r**3 + 0*r**5 + 2*r + 0*r**2 + 0 + 1/105*r**6. Suppose t(q) = 0. Calculate q.
-1, 0, 1
Let i = 12 + -10. Determine n so that -12*n - 4 + 6*n**4 + 12*n**3 + 3*n**4 - 4*n**4 - n**i = 0.
-2, -1, -2/5, 1
Let a(v) = v**3 + 4*v**2 - 2*v - 5. Let h be a(-4). Let c(n) = -n**3 + n**2 + n + 4. Let y be c(0). Factor -y*i**2 + i**2 + i - 2*i - i**4 - i**h - 2*i**3.
-i*(i + 1)**3
Let w = -65339/180 - -363. Let q(t) be the third derivative of 2/9*t**3 + w*t**5 + 2*t**2 + 0*t + 0 - 1/18*t**4. Factor q(f).
(f - 2)**2/3
Let z be ((-1)/(-2))/(5/20). Suppose 0 = -y - f + 1, z*y - 8 = -f + 5*f. Factor 1/5*v**y + 1/5 - 2/5*v.
(v - 1)**2/5
Let d(h) = h**3 - h**2. Let g(m) be the second derivative of -3*m**5/10 - m**3/3 + m. Let j(v) = -4*d(v) - g(v). Factor j(x).
2*x*(x + 1)**2
Suppose 14 + 7 = 7*u. Let 9/2*j**u + 3 - 3/2*j**4 - 9/2*j - 3/2*j**2 = 0. What is j?
-1, 1, 2
Let i = -251 - -1013/4. Factor 1/2 + i*u + 7/4*u**2.
(u + 1)*(7*u + 2)/4
Let u be ((-21)/2)/((-2)/4). Let k = u - 19. Factor 1/3*s**k + 1/3 + 2/3*s.
(s + 1)**2/3
Suppose 10 = 5*g - 3*g. Suppose g*a + 30 = 5*w, -2*a = -w + 2*w + 3. Determine n, given that 3/4*n**4 + 0 + 0*n + 3*n**3 + w*n**2 = 0.
-2, 0
Let z be 47402/(-30) + (-2)/(-3). Let q = z - -1589. What is g in 38/5*g**3 - 82/5*g**2 + 18/5*g**4 + q*g - 8/5 - 14/5*g**5 = 0?
-2, 2/7, 1
Factor 0 + 0*d**3 - 6/13*d**2 - 4/13*d + 2/13*d**4.
2*d*(d - 2)*(d + 1)**2/13
Let z(m) = -11*m**2 - 11*m - 2. Let h(s) = s**2. Suppose -3*d + 20 = 2. Let o(v) = d*h(v) + 3*z(v). Factor o(g).
-3*(g + 1)*(9*g + 2)
Determine x, given that -2*x**2 + 2*x**5 + 4*x**2 - 2*x**3 + 12*x**4 + 0*x**3 - 14*x**4 = 0.
-1, 0, 1
Factor 0 - 1/6*w**2 - 1/2*w.
-w*(w + 3)/6
Let l(v) be the third derivative of v**7/1995 - 2*v**5/285 - 35*v**2. Factor l(a).
2*a**2*(a - 2)*(a + 2)/19
Let q(x) be the second derivative of x**6/10 - x**5/20 - 5*x**4/12 + x**3/6 + x**2 - 3*x. Factor q(n).
(n - 1)**2*(n + 1)*(3*n + 2)
Let r = 17 - 14. Solve 4*x**3 - 5*x**3 + r*x**4 - 5*x**4 + 5*x**3 - 2*x**2 = 0 for x.
0, 1
Let r(c) = -c**2 - c + 1. Let p(t) = 7*t**2 + 8*t - 5. Let i(o) = 5*p(o) + 30*r(o). Factor i(u).
5*(u + 1)**2
Let k be ((-32)/48)/(2/(-12)). Suppose 2*m = k*u + 10, -17 + 2 = 5*u - 3*m. Factor u + 1/4*i**2 + 1/2*i.
i*(i + 2)/4
Let r(i) be the first derivative of -i**3 - 21*i**2/2 - 18*i + 22. Solve r(y) = 0 for y.
-6, -1
Suppose -108 = -5*f + 2. Determine w, given that -8*w - 18 + 5*w**2 + f - 2*w**2 = 0.
2/3, 2
Determine x so that 2*x**5 + x**2 + 8*x**4 - 6*x**5 + 3*x - 9*x**2 + x = 0.
-1, 0, 1
Determine h so that -4/11*h + 10/11*h**2 - 16/11 - 2/11*h**3 = 0.
-1, 2, 4
Suppose -2*k - 34 = d, 2*k = 4*k - 2*d + 28. Let t = k - -18. Solve 1/3*j**3 - 1/3*j**4 + 0 + 1/3*j**t - 1/3*j = 0.
-1, 0, 1
Find y such that 0 - 1/3*y**5 + 0*y + 0*y**2 + 0*y**4 + 1/3*y**3 = 0.
-1, 0, 1
Let j(n) = -n**2 + 2*n - 1. Let w(b) = -3*b**2 + 5*b - 2. Let z(a) = 5*j(a) - 2*w(a). Find v such that z(v) = 0.
-1, 1
Let w = 22 + -4. Suppose 3*m = -3*y + 7*y - 6, 3*m - w = -4*y. Determine u so that -2 + u**2 + 0*u - 3*u**m + 3*u**2 + u = 0.
-2, 1
Let v(b) be the first derivative of 2*b**6/15 + 3*b**5/5 + 2*b**4/3 - 4*b - 5. Let o(s) be the first derivative of v(s). Solve o(c) = 0.
-2, -1, 0
Suppose -1 = -3*k + n, 8 = 4*k + 2*n - 10. Suppose -3*z = -5*c + 10, 5*c - 6*z + k*z = 10. Factor 2*o**c - 4/3 + 2/3*o.
2*(o + 1)*(3*o - 2)/3
Let l(g) be the third derivative of -1/1440*g**6 + 1/96*g**4 + 0 + 0*g + 0*g**5 + g**2 + 1/3*g**3. Let f(s) be the first derivative of l(s). Factor f(j).
-(j - 1)*(j + 1)/4
Let r(d) = -10*d**3 + 50*d**2 - 175*d + 125. Let z(c) = -c**3 - c**2. Let j(u) = -r(u) + 5*z(u). Factor j(s).
5*(s - 5)**2*(s - 1)
Let b(t) be the first derivative of 4 - 1/2*t + 1/20*t**5 + 1/12*t**3 - 3/8*t**2 + 3/16*t**4. Factor b(y).
(y - 1)*(y + 1)**2*(y + 2)/4
Factor 15*c**2 + 5/2*c**3 - 5/2*c - 15.
5*(c - 1)*(c + 1)*(c + 6)/2
Let g be (-17)/(-136) - (-1)/(-8). Determine j, given that -1/6*j**2 + g + 0*j = 0.
0
Factor -9*c - 38 - 4*c**2 + 22 - 7*c.
-4*(c + 2)**2
Let m(a) = -a**2 - 6*a. Let j = -19 + 13. Let h be m(j). Find s such that h*s**2 + 2*s**5 + 9*s**3 + s - 7*s**4 - s**2 - 4*s**2 = 0.
0, 1/2, 1
Suppose -19*p + 0 = -76. Suppose 2*u**p + 2/5 - 2*u - 2/5*u**5 - 4*u**3 + 4*u**2 = 0. What is u?
1
Let h(q) = -14*q**5 + 12*q**4 + 32*q**3 + 6*q**2. Let z(k) = 5*k**5 - 4*k**4 - 11*k**3 - 2*k**2. Let p(r) = 6*h(r) + 17*z(r). Factor p(d).
d**2*(d + 1)**2*(d + 2)
Let c(s) be the second derivative of -s**5/20 - s**4/12 + s**3/3 + s**2 - 4*s. Let f be c(-2). Factor 2*y + 1/2*y**2 + f.
(y + 2)**2/2
Let a(w) be the third derivative of w**7/1155 + w**6/132 + 3*w**5/110 + 7*w**4/132 + 2*w**3/33 - 11*w**2. Factor a(x).
2*(x + 1)**3*(x + 2)/11
Let p(x) = -x**4 - x**3 + x**2 - 1. Let o(i) = -10*i**4 + 2*i**3 + 22*i**2 - 32*i - 6. Let z(b) = -o(b) + 6*p(b). Factor z(u).
4*u*(u - 2)**2*(u + 2)
Let v(r) be the third derivative of r**7/2100 - r**5/300 + r**3/2 - 3*r**2. Let w(l) be the first derivative of v(l). Factor w(m).
2*m*(m - 1)*(m + 1)/5
Determine y, given that -4/3*y - 4/3*y**5 - 1/3*y**3 + 4*y**2 - 4*y**4 + 0 = 0.
-2, 0, 1/2
Let f(k) = -3*k**3 + k**2 - 10*k - 7. Let v(n) be the second derivative of n**5/10 - n**4/12 + 7*n**3/6 + 5*n**2/2 - n. Let r(l) = 5*f(l) + 7*v(l). Factor r(o).
-o*(o + 1)**2
Let k(x) be the third derivative of 0*x**3 + 1/60*x**6 + 11/240*x**5 - 1/40*x**7 - 5*x**2 + 1/48*x**4 + 0 + 0*x. Let k(s) = 0. Calculate s.
-1/3, -2/7, 0, 1
Let j(w) = -18*w + 9. Let s(l) = -l**3 - l**2 + 35*l - 18. Let n(c) = 5*j(c) + 3*s(c). What is t in n(t) = 0?
-3, 1
Let c(d) be the second derivative of d**6/15 - d**5/10 - d**4/6 + d**3/3 - d. Determine x, given that c(x) = 0.
-1, 0, 1
Let u = -21 + 11. Let g = -7 - u. Factor -4*a + g*a**2 + 3*a + 4*a.
3*a*(a + 1)
Suppose 2 + 4 = 2*p. Suppose -3*d + 39 = -p*t, -d + 35 = 4*d + t. Factor o**2 + 2*o + 18*o**3 + d*o**4 + 5*o**2 + 6*o**2.
2*o*(o + 1)**2*(4*o + 1)
Let h(z) be the first derivative of -z**6/3 + 4*z**5/5 - 4*z**3/3 + z**2 - 16. Factor h(f).
-2*f*(f - 1)**3*(f + 1)
Let y(z) = -4*z**3 + 18*z**2 + 66*z + 38. Let h(q) = -4*q**3 + 19*q**2 + 65*q + 37. Let r(o) = 6*h(o) - 5*y(o). Determine x, given that r(x) = 0.
-1, 8
Suppose i + 4 = -0*i, -5*f + i = -19. Let n be (4 + 3 + -6)/f. Factor 0*r**3 - 2/3*r**2 - n*r + 1/3*r**5 + 0 + 2/3*r**4.
r*(r - 1)*(r + 1)**3/3
Factor 2*j**4 - 2*j**2 - 205*j**5 + 106*j**5 + j**3 + 98*j**5 + 0*j**3.
-j**2*(j - 2)*(j - 1)*(j + 1)
Let x(o) be the third derivative of o**9/181440 + o**8/15120 + o**7/3024 + o**6/1080 + o**5/30 - 2*o**2. Let v(l) be the third derivative of x(l). Factor v(q).
(q + 1)**2*(q + 2)/3
Suppose 0 = r + 4*r. Suppose r = 7*t - 2*t - 10. Determine s, given that 3/2*s**4 - 2*s**5 + 0*s**t + 1/2*s**3 + 0 + 0*s = 0.
-1/4, 0, 1
Let m = 51 - 48. Let q(v) be the third derivative of 0*v + 0 - m*v**2 + 1/360*v**5 + 1/18*v**3 + 1/48*v**4. Factor q(x).
(x + 1)*(x + 2)/6
Let s = 106 - 106. Let y(r) be the third derivative of 0*r**4 - 7/600*r**6 + 1/150*r**5 + 0 + s*r**3 + 0*r - r**2. Factor y(c).
-c**2*(7*c - 2)/5
Let a(f) be the first derivative of -3*f + 1/10*f**5 + 1/3*f**4 + 0*f**2 - 2 + 1/3*f**3. Let b(t) be the first derivative of a(t). Factor b(h).
2*h*(h + 1)**2
Suppose 0 = 4*u + u - 20. Suppose 7*w**2 - 3*w**u - 12*w**5 + 17*w**3 - 4 + 3*w**5 - 6*w + 0*w**4 - 2*w = 0. Calculate w.
-1, -2/3, 1
Factor -3/4*i**2 + 3/4 + 0*i.
-3*(i - 1)*(i + 1)/4
Let n(t) = -13*t**2 + 4*t - 11. Let c(k) = 7*k**2 - 2*k + 6. Suppose 4*q + 29 = -2*b - 9, 2*b - 2*q + 14 = 0. Let v(x) = b*c(x) - 6*n(x). Factor v(h).
h*(h - 2)
Factor 6*g**2 - 2/3*g**4 - 2/3*g**3 - 22/3*g + 8/3.
-2*(g - 1)**3*(g + 4)/3
Let q(n) be the third derivative of -n**8/672 + n**7/140 - n**6/80 + n**5/120 + 2*n**2. Factor q(w).
-w**2*(w - 1)**3/2
Let w(b) be the first derivative of -3*b**4/44 - 5*b**3/33 + 8*b**2/11 + 12*b/11 + 15. Solve w(c) = 0 for c.
-3, -2/3, 2
Let i(a) = a**2 - 3*a - 6. Let z be i(5). Solve 4 - z*f**4 - 5 - 4*f**5 + 1 = 0.
-1, 0
Suppose -5*r + 14 + 66 = 0. Factor -5*y - r + 4*y - 7*y - y**2.
-(y + 4)**2
Let i = 388 - 775/2. Factor -16*x - 4*x**3 - 12*x**2 - 8 - i*x**4.
-(x +