33. Let h(k) = -k**4 - 4*k**3 + k**2 + 4*k + 4. Let u(d) = 4*c(d) - 33*h(d). Factor u(z).
-3*z**2*(z - 1)*(z + 1)
Let y = 7 - 5. What is b in -4*b - y*b**3 - b**2 - 1 + 2 + 3*b**2 + 3*b**2 = 0?
1/2, 1
Let h(c) = 11*c**5 - 12*c**4 - 9*c**3 + 2*c**2 - 8*c - 8. Let y(p) = -p**5 + p**4 + p**3 + p + 1. Let g(q) = -3*h(q) - 24*y(q). Solve g(r) = 0.
-2/3, 0, 1
Let i = 415/1692 + 2/423. Let q(c) be the third derivative of 0 + 3*c**2 + 0*c - 1/2*c**3 - i*c**4 - 1/20*c**5. Factor q(s).
-3*(s + 1)**2
Suppose 0 = -4*y + 4*a - 7 - 1, y = 4*a - 8. Find g such that -1/4*g**2 + 1/4 + y*g = 0.
-1, 1
Factor 3*m + 9/4 + 3/4*m**2.
3*(m + 1)*(m + 3)/4
Let t(w) be the first derivative of 2/15*w**3 + 0*w**2 + 3 - 2/5*w. Factor t(v).
2*(v - 1)*(v + 1)/5
Factor 1/2*v**4 + 0*v - 3/4*v**5 + 0 + 0*v**2 + 1/4*v**3.
-v**3*(v - 1)*(3*v + 1)/4
Suppose 0*j + 7 = -c + 2*j, 5*j - 16 = 3*c. Find z such that 0*z - 1/4*z**4 + 0 - 1/4*z**2 + 1/2*z**c = 0.
0, 1
Let w(p) = -4*p**3 - 4*p**2 + 6*p + 6. Let k(a) = -7*a**3 - 7*a**2 + 11*a + 11. Let m(f) = -6*k(f) + 11*w(f). Factor m(h).
-2*h**2*(h + 1)
Let q(n) be the third derivative of -1/112*n**8 + 0*n + 0 + 0*n**5 + 2*n**2 + 2/35*n**7 + 0*n**3 - 3/40*n**6 + 0*n**4. Factor q(b).
-3*b**3*(b - 3)*(b - 1)
Suppose v - 4 = 14. Let r = v - 18. Determine l so that 2/7*l**2 + 2/7*l + r = 0.
-1, 0
Let k be (-34)/(-16) + (-15)/120. Let -i + 1 + 1/4*i**k = 0. What is i?
2
Let r(q) be the second derivative of q**4/78 - 7*q**3/39 + 12*q**2/13 + 3*q. Let r(l) = 0. What is l?
3, 4
Suppose 10/11*b**4 + 14/11*b**3 - 8/11 - 16/11*b - 2/11*b**2 + 2/11*b**5 = 0. What is b?
-2, -1, 1
Let q(o) = -o**3 - 7*o**2 + 9*o + 9. Suppose 8 = -3*m - z - 3*z, 5*z - 28 = m. Let v be q(m). Let 3*w - w**2 + 0*w**2 + v - w**3 - 2*w = 0. Calculate w.
-1, 1
Suppose -q + 2*t = -10, 10 = -4*q + 2*t + 26. Let -8*y**3 + 0*y - 2*y**4 - 12*y**q - 8*y - 2 + 0*y**4 = 0. What is y?
-1
Let i(v) be the first derivative of -1 + 0*v**2 + 0*v - 1/3*v**3 - 1/12*v**4. Factor i(u).
-u**2*(u + 3)/3
Suppose 2*k - 3*y - 10 = -0*k, k - 5 = 4*y. Let v(d) be the second derivative of 4*d + 1/6*d**3 + 1/12*d**4 - 1/2*d**2 + 0 - 1/20*d**k. Factor v(i).
-(i - 1)**2*(i + 1)
Suppose 172 = 5*p - 4*g, -3*p - 2*p - g + 182 = 0. Let f be (p/(-60))/(2/(-4)). Factor f*n**2 + 2/5 + 6/5*n + 2/5*n**3.
2*(n + 1)**3/5
Let 8*q**2 - 16*q**2 + 4 + 5*q**2 + q**3 = 0. Calculate q.
-1, 2
Let u be (1/3*0)/(-2). Suppose 5*d + 7 = -t - 7, u = 4*t + 3*d - 12. Factor -6*i**3 - t*i**4 - 4*i**5 + 8*i**2 + 2*i**5 - 10*i**2.
-2*i**2*(i + 1)**3
Let t(b) be the first derivative of b**5/55 - 5*b**4/44 + 5*b**3/33 + 5*b**2/22 - 6*b/11 + 18. Let t(x) = 0. Calculate x.
-1, 1, 2, 3
Let r(f) = f. Let u(o) be the first derivative of 2*o**3 - 8*o**2 - 2*o + 1. Let z(i) = 12*r(i) + u(i). Factor z(a).
2*(a - 1)*(3*a + 1)
Let r be (-1)/((-3)/24*2). Suppose -2*w - w = b + 4, -4*b + r = 2*w. Factor -2 - 25/2*x**b - 10*x.
-(5*x + 2)**2/2
Let x(p) be the first derivative of p**3 + 12*p**2 + 36*p - 12. Factor x(a).
3*(a + 2)*(a + 6)
Let n(b) = -2*b**4 + 3*b + 3*b + 0*b**4 - b**3 - b**5 - 4*b. Let t(z) = 4*z**5 + 6*z**4 + 4*z**3 - 7*z. Let l(r) = 14*n(r) + 4*t(r). Factor l(u).
2*u**3*(u - 1)**2
Let n be -1 - (6 + -3)/1. Let x(j) = j**3 + 3*j**2 - 3*j + 4. Let s be x(n). Factor -1/2*w**5 + 0*w**4 - 1/2*w + 0 + w**3 + s*w**2.
-w*(w - 1)**2*(w + 1)**2/2
Let s(a) be the first derivative of 0*a - 1/3*a**2 + 2/27*a**3 + 4. Factor s(r).
2*r*(r - 3)/9
Let -3*c + 69*c**2 - c - 73*c**2 = 0. Calculate c.
-1, 0
Let q(z) be the second derivative of -1/12*z**4 - 9/2*z**2 - 4*z - z**3 + 0. Determine x so that q(x) = 0.
-3
Let f(c) = -c**3 - 4*c**2 + 10*c + 4. Let q be f(-8). Let u be 159/q + (-2)/15. Find m such that -1/4 + 5/4*m**2 + 3/4*m**3 - u*m - m**4 = 0.
-1, -1/4, 1
Let u(y) be the third derivative of -y**7/70 + y**5/5 - 4*y**2. Factor u(d).
-3*d**2*(d - 2)*(d + 2)
Factor -44/13*f - 2/13*f**2 - 242/13.
-2*(f + 11)**2/13
Let g = 80 - 78. Factor 1/5*z - 4/5*z**g + 0 + 3/5*z**3.
z*(z - 1)*(3*z - 1)/5
Determine a so that 534*a**2 - 10*a - 5*a**4 - 559*a**2 - 12*a**3 - 8*a**3 = 0.
-2, -1, 0
Let o(s) = -8*s**2 - 6*s - 8. Let z(k) = 2*k - 12. Let b be z(8). Let q(l) = 3 + 0*l + 3*l**2 - b + 4 + 2*l. Let y(a) = 4*o(a) + 11*q(a). Solve y(r) = 0 for r.
1
Let a(y) = 6*y**4 - y**3 - y**2 + y + 1. Let u(q) = 5*q**4 - 2*q**2 + 1. Let j(k) = -2*a(k) + 3*u(k). Factor j(i).
(i - 1)*(i + 1)**2*(3*i - 1)
Suppose z + 1 + 2 = s, 0 = -4*s - 2*z + 18. Factor 4/5*u**3 - 4/5*u - 2/5*u**s + 2/5 + 0*u**2.
-2*(u - 1)**3*(u + 1)/5
Suppose -4*p = -17 + 1. Let v(i) be the second derivative of 0 + 1/18*i**p + 2/9*i**3 - i + 1/3*i**2. Factor v(k).
2*(k + 1)**2/3
Let p(n) = -7*n**4 - n**3 + 3*n**2. Let d(a) = -4*a**2 - 3*a**4 + 2*a**2 + 6*a**4 + 3*a**4. Let w(u) = 5*d(u) + 4*p(u). Solve w(c) = 0.
0, 1
Let r be 14/63 - 43/(-9). Suppose 0*u - u - 3 = 0, 5*f - 3*u - 24 = 0. Suppose -4/9*m**2 + 4/9 + 0*m**4 - 8/9*m**f + 2/3*m + 2/9*m**r = 0. Calculate m.
-1, 1, 2
Suppose -14*d + 9*d + 4*s = -37, 4*s + 7 = -d. Factor 2/7*r**2 - 2/7*r**3 + 0 + 0*r + 2/7*r**d - 2/7*r**4.
2*r**2*(r - 1)**2*(r + 1)/7
Let s(t) = 5*t**2 - 5*t + 4. Let q(r) = -6*r**2 + 6*r - 5. Let f(w) = -4*q(w) - 5*s(w). Suppose f(a) = 0. What is a?
0, 1
Suppose 0 = -2*a - 5 - 3. Let t = a + 9. Factor 4*c**4 + 0*c**4 + c**2 - t*c**4.
-c**2*(c - 1)*(c + 1)
Suppose 4*l - 15 = u, -4*u = -0*u + 4*l. Let c(j) = j**3 + 2*j**2 - 5*j - 3. Let m be c(u). Factor v**4 - 5*v**m + 7*v**3 + v**4.
2*v**3*(v + 1)
Determine p so that 1/3*p**2 + 0 - 2/3*p**4 + 1/3*p**3 + 0*p = 0.
-1/2, 0, 1
Let z(c) = 10*c**3 + 50*c**2 - 10*c - 55. Let i(o) = -5*o**3 - 25*o**2 + 5*o + 27. Let u(d) = 5*i(d) + 2*z(d). Factor u(q).
-5*(q - 1)*(q + 1)*(q + 5)
What is j in -3*j**2 + 3*j - 3*j + 2*j + j + 3 - 3*j**3 = 0?
-1, 1
Let u(x) be the first derivative of x**3/3 - 5*x**2/2 - 4*x - 8. Let o be u(6). Factor 8/9*v**3 - 2/9*v + 0 + 0*v**o.
2*v*(2*v - 1)*(2*v + 1)/9
Let d(a) be the third derivative of -a**7/2520 + a**6/360 - a**4/12 - 3*a**2. Let r(u) be the second derivative of d(u). Factor r(h).
-h*(h - 2)
Let g(m) be the second derivative of 3/20*m**4 + 0 + m + 3/5*m**2 + 1/2*m**3. Find y such that g(y) = 0.
-1, -2/3
Let x = 1849/84 - 22. Let i(h) be the third derivative of 1/420*h**6 - 1/105*h**5 + 0 + 0*h + 0*h**3 + x*h**4 + h**2. Factor i(q).
2*q*(q - 1)**2/7
Let q(x) = 7*x**3 - 7*x**2 - 7*x + 7. Let m(v) = 8*v**3 - 8*v**2 - 8*v + 8. Let c(r) = 5*m(r) - 6*q(r). Factor c(l).
-2*(l - 1)**2*(l + 1)
Let a(f) be the third derivative of -f**5/330 + 3*f**4/22 - 27*f**3/11 - 15*f**2. Factor a(l).
-2*(l - 9)**2/11
Let y(h) = h**4 - 4*h**3 - 2*h**2 + 2*h - 1. Let q(m) be the first derivative of m**5/5 - m**4/4 - m**3/3 - m + 1. Let d(z) = -2*q(z) + y(z). Factor d(b).
-(b - 1)*(b + 1)**3
Let x be (-9)/2 + 4 + 2. Determine w so that -w**2 + 0*w - 5/2*w**3 - x*w**4 + 0 = 0.
-1, -2/3, 0
Let z(t) be the first derivative of 3*t**4/14 - 2*t**3/7 - 3*t**2/7 + 6*t/7 - 25. Suppose z(v) = 0. Calculate v.
-1, 1
Let h(f) = f**2 + 76*f + 324. Let n(t) = -4*t**2 - 229*t - 971. Let j(w) = -11*h(w) - 4*n(w). Factor j(i).
5*(i + 8)**2
Suppose 4*u - 4*u + 2*u = 0. Factor u*v + 0*v**2 + 2/9*v**4 + 2/9*v**3 + 0.
2*v**3*(v + 1)/9
Let a(u) be the second derivative of -u**6/120 - u**5/40 + u**4/4 - u**3/2 - 4*u. Let x(h) be the second derivative of a(h). Find f, given that x(f) = 0.
-2, 1
Let g = -35 - -176/5. Let d(h) = -h**2 - 5*h + 3. Let a be d(-5). Let 0 - g*r - 2/5*r**2 - 1/5*r**a = 0. Calculate r.
-1, 0
Let i(n) be the first derivative of -3*n**4/8 + 3*n**3/2 - 3*n**2/2 - 23. Factor i(f).
-3*f*(f - 2)*(f - 1)/2
Factor -1/2*b - 3/4 + 1/4*b**2.
(b - 3)*(b + 1)/4
Let u(q) = q + 5. Let x be u(-3). Solve -j**x + 2*j**4 - j**2 - 2*j**3 + 2*j**2 = 0 for j.
0, 1
Let p(v) = 12*v**4 - 15*v**3 - 7*v**2 + 103*v - 36. Let q(s) = s**4 + s**3 + s. Let l(t) = 3*p(t) - 21*q(t). Let l(r) = 0. What is r?
-2, 2/5, 3
Find l such that 5/3*l**2 + 11/3*l + 2/3 = 0.
-2, -1/5
Suppose 0 = -f - q + 2, -3*f - f = -5*q + 1. Let d = f - 1. Factor 4/5*v**3 + 2/5*v + 6/5*v**2 + d.
2*v*(v + 1)*(2*v + 1)/5
Let u be 69/(-12) - -2 - 0. Let x = 4 + u. Find v, given that -1/4*v**2 - 1/4*v**3 + x*v + 0 + 1/4*v**4 = 0.
-1, 0, 1
Let l be 3 + (788/16)/1. Let o = l - 52. Factor -o - 1/2*y + 3/4*y**2 + y**3 - y**4.
-(y - 1)**2*