Let k(q) be the first derivative of 11*q**4 - 4*q**3/3 - 68*q**2 + 96*q + 182. Factor k(u).
4*(u - 1)*(u + 2)*(11*u - 12)
Let g(v) be the second derivative of v**6/60 - v**4/12 + 11*v**2/2 + 3*v. Let p(o) be the first derivative of g(o). Factor p(x).
2*x*(x - 1)*(x + 1)
Let l(b) be the third derivative of 8 + 1/336*b**8 + 1/30*b**5 - 3/2*b**3 - b**2 + 7/60*b**6 + 1/30*b**7 + 0*b - 5/8*b**4. Factor l(a).
(a - 1)*(a + 1)**2*(a + 3)**2
Let m(n) be the first derivative of -14*n**5/5 + 267*n**4 - 6840*n**3 + 2888*n**2 - 193. Factor m(j).
-2*j*(j - 38)**2*(7*j - 2)
Let h(r) be the second derivative of 9*r**6/20 - 3*r**5/20 - 9*r**4/8 + r**3/2 - r + 102. Determine p, given that h(p) = 0.
-1, 0, 2/9, 1
Let z = -5486/17 + 322. Let g = 128/85 + z. Find f such that -16/5*f - 12/5 - g*f**2 = 0.
-3, -1
Let j be 45/20 + (1 - 10/8). Let b be 1/5 - (-5 + (-219)/(-45)). Solve 2/3*x + 1/3*x**j + b = 0.
-1
Factor 12*t + 162 + 2/9*t**2.
2*(t + 27)**2/9
Suppose -82*i + 234 = -4*i. Solve -2/3*m - 2/3 + 2/3*m**2 + 2/3*m**i = 0.
-1, 1
Let d(g) be the first derivative of -g**5/8 - 35*g**4/8 - 245*g**3/4 - 1715*g**2/4 + 3*g - 15. Let x(t) be the first derivative of d(t). Factor x(s).
-5*(s + 7)**3/2
Let j be ((-24)/(-28)*-2)/(2/(-21)). Find q such that 995 - 990 + 10*q**2 + 3*q - j*q = 0.
1/2, 1
Let t(x) be the third derivative of x**8/112 - x**6/20 + x**4/8 + 85*x**2. Factor t(m).
3*m*(m - 1)**2*(m + 1)**2
Let j(c) = -86*c - 2752. Let f be j(-32). Let f - 4/5*p**2 + 0*p = 0. Calculate p.
0
Let b = -60899/60 - -1015. Let o(l) be the third derivative of 0*l + b*l**6 + 0*l**3 - 1/12*l**4 + 1/30*l**5 + 4*l**2 + 0 - 1/105*l**7. Factor o(q).
-2*q*(q - 1)**2*(q + 1)
Let s(u) be the first derivative of 4 + 0*u + 2/25*u**5 - 1/5*u**2 - 3/10*u**4 + 2/5*u**3. Factor s(w).
2*w*(w - 1)**3/5
Suppose -9*k + 3*k = -90. Let n be (-6)/4 + k/2 - 4. Solve -2/15 + 0*m + 2/15*m**n = 0 for m.
-1, 1
Let k(m) be the third derivative of -m**8/1848 - m**7/231 + m**6/330 + 14*m**5/165 + 2*m**4/33 - 32*m**3/33 - 147*m**2. Solve k(t) = 0.
-4, -2, 1, 2
Factor 0 + 1/5*n**3 + 5*n - 2*n**2.
n*(n - 5)**2/5
Let m(s) = -s**5 + s**4 - 2*s**3 + 2*s**2 - 2*s - 2. Let j(o) = -2*o**5 - 3*o**3 + 5*o**2 - 5*o - 5. Let y(t) = 2*j(t) - 5*m(t). Factor y(x).
x**3*(x - 4)*(x - 1)
Let h(r) be the first derivative of 2*r**5/35 + 2*r**4 - 118*r**3/21 + 30*r**2/7 + 134. Solve h(n) = 0 for n.
-30, 0, 1
Let g(v) be the first derivative of -v**3 - 6*v**2 - 9*v - 13. Factor g(f).
-3*(f + 1)*(f + 3)
Let j(h) be the third derivative of -h**5/80 + 5*h**4/16 - 2*h**3 - 16*h**2 - 3. Factor j(w).
-3*(w - 8)*(w - 2)/4
Let g(h) be the first derivative of -h**5/5 + h**4/2 + 5*h**3 + 2*h**2 - 20*h - 183. Factor g(l).
-(l - 5)*(l - 1)*(l + 2)**2
Let m(t) be the second derivative of t**6/10 + 3*t**5/5 - 11*t**4/4 + 3*t**3 - 2*t + 1. Factor m(z).
3*z*(z - 1)**2*(z + 6)
Let j = -119/2 + 43/4. Let d = 49 + j. Solve 1/4 + 3/4*o**2 + 3/4*o + d*o**3 = 0.
-1
Suppose z = 5*z + 20. Let m(w) = 3*w**3 - w**2. Let q(i) = -7*i**3 + 3*i**2. Let y(l) = z*m(l) - 2*q(l). Factor y(o).
-o**2*(o + 1)
Let b(d) = -d**3 - 8*d**2 + 10*d + 11. Let s(h) = -h**2 + 3*h - 5. Let m be s(4). Let r be b(m). Factor -4*j - 11*j**2 + 4*j**3 + 8 + 10*j**r - 7*j**2.
4*(j - 2)*(j - 1)*(j + 1)
Let v = 66897/8 + -8362. Factor -v*t**2 - 1/4*t + 3/8.
-(t - 1)*(t + 3)/8
Let r(o) = -16*o**3 + 32*o**2 + 2. Let b be r(2). Let j(n) be the first derivative of 4/9*n**3 + 0*n + 6 + 0*n**b + 1/15*n**5 - 1/3*n**4. Solve j(f) = 0.
0, 2
Let d(o) = 6*o**5 + 32*o**4 + 90*o**3 + 44*o**2. Let v(i) = 2*i**5 + 11*i**4 + 30*i**3 + 15*i**2. Let z(q) = -3*d(q) + 10*v(q). What is m in z(m) = 0?
-3, -1, 0
Let z(m) = -5*m**3 + 10*m**2. Suppose 6 = -4*g + 2. Let c(h) = h**2. Let w(u) = g*z(u) + 25*c(u). Factor w(l).
5*l**2*(l + 3)
Let t(n) be the second derivative of -1/2*n**5 + 0 + 8*n**2 - n**4 + 4/3*n**3 + 34*n - 1/15*n**6. Find c, given that t(c) = 0.
-2, 1
Let z(h) be the first derivative of 0*h - 12 + 3/20*h**4 - 3/10*h**2 + 0*h**3. Factor z(k).
3*k*(k - 1)*(k + 1)/5
Factor 1/3*p**2 + 0*p + 0 - 4/3*p**3.
-p**2*(4*p - 1)/3
Let f(m) be the third derivative of m**5/60 - m**4/24 - m**3/3 + 154*m**2. Suppose f(a) = 0. Calculate a.
-1, 2
Let -2*l - 4 - 2*l**3 - 8*l**2 + 12*l**2 - 2*l**4 + 5*l**3 - l + 2 = 0. What is l?
-1, -1/2, 1, 2
Let f(m) be the first derivative of -3*m**5/5 - 27*m**4/4 - 24*m**3 - 24*m**2 - 50. Factor f(l).
-3*l*(l + 1)*(l + 4)**2
Let f be 1*(4/(-30) - 10/(-30)). Let m(g) be the second derivative of 0 - g - 1/30*g**4 - 2/5*g**2 - f*g**3. Factor m(y).
-2*(y + 1)*(y + 2)/5
Let v(r) = 20*r**4 - 12*r**3 - 4*r**2 + 12*r + 8. Let i(c) = -7*c**4 + 4*c**3 + c**2 - 4*c - 3. Let s = 41 - 49. Let k(m) = s*i(m) - 3*v(m). Factor k(t).
-4*t*(t - 1)**2*(t + 1)
Let i = 113248/5 + -22649. Factor -i*u**2 + 1/5*u**4 + 3/5*u**3 - 6/5 - 11/5*u.
(u - 2)*(u + 1)**2*(u + 3)/5
Let k(p) be the second derivative of 10/11*p**3 + 0 - 5*p + 1/22*p**4 + 75/11*p**2. Factor k(x).
6*(x + 5)**2/11
Let t = 73 + -68. Let i(s) be the second derivative of -3/20*s**t + 3*s + 0 + 0*s**4 + 0*s**2 + 1/2*s**3. Factor i(b).
-3*b*(b - 1)*(b + 1)
Let a(h) = 5*h**4 - h**3 + 8*h**2 - 3*h + 7. Let v(y) = 4*y**4 - y**3 + 8*y**2 - 2*y + 6. Let o(b) = 6*a(b) - 7*v(b). Factor o(f).
f*(f - 2)*(f + 2)*(2*f + 1)
Let o = 6877 + -13747/2. Factor 2 - o*j**2 + 3/2*j**3 + 0*j.
(j - 2)*(j - 1)*(3*j + 2)/2
Let t(g) be the second derivative of g**7/84 + g**6/40 - g**5/40 - g**4/12 + g**2/8 + 6*g + 5. Suppose t(c) = 0. What is c?
-1, 1/2, 1
Let q(f) be the third derivative of 0*f**3 + 0*f - 1/120*f**6 + 6*f**2 - 1/24*f**4 + 0 - 1/30*f**5. Factor q(j).
-j*(j + 1)**2
Let t(y) be the first derivative of -y**4/4 + 2*y**3 + y**2/2 - 6*y - 105. Suppose t(z) = 0. What is z?
-1, 1, 6
Suppose 10*l - 8*l = 3*g - 27, -5*g - l = -19. Factor -1/2*o**4 + 0 - 1/6*o**g + 0*o**2 - 1/3*o**3 + 0*o.
-o**3*(o + 1)*(o + 2)/6
Let w(u) = -9*u**4 - 9*u**3 - 29*u**2 + 54. Let y(x) = 5*x**4 + 4*x**3 + 14*x**2 - 27. Let o(z) = 4*w(z) + 7*y(z). Find p such that o(p) = 0.
-3, 1
Let p(s) = -1. Let f(g) = -g**3 + 3*g**2 + 4*g - 9. Let b be 1/(-7) + (-378)/98. Let c(m) = b*f(m) + 36*p(m). Let c(q) = 0. Calculate q.
-1, 0, 4
Let y(w) = -w**3 + 21*w**2 + 2*w - 42. Let m be y(21). Let u(f) = -4*f + 2. Let d be u(-2). Factor 3*g**4 + 0 - 13*g**2 + d*g**2 + m.
3*g**2*(g - 1)*(g + 1)
Suppose 0 = 5*d - 5*x - 620, 0 = 2*d + 4*x - 274 + 32. Let r = -123 + d. Factor 1/2*o**2 - 1/4*o - 1/4*o**3 + r.
-o*(o - 1)**2/4
Let w(o) be the first derivative of -2*o**5/25 + 3*o**4/10 + 6*o**3/5 - 27*o**2/5 + 75. Factor w(u).
-2*u*(u - 3)**2*(u + 3)/5
Factor -65/2*i - 5/2*i**4 + 0 + 125/2*i**2 - 55/2*i**3.
-5*i*(i - 1)**2*(i + 13)/2
Suppose 4*n = 3*p - 3, 4*n - 94 + 57 = -5*p. Solve 0 - 1/5*a**4 + a**2 - 3/5*a - 1/5*a**n = 0 for a.
-3, 0, 1
Let z(q) = 2*q**3 + q**2 - 1. Let a(t) = -1029*t**5 - 9457*t**4 - 1434*t**3 + 3165*t**2 + 1312*t + 147. Let m(f) = a(f) + 3*z(f). What is b in m(b) = 0?
-9, -2/7, 2/3
Let z be (-1 + (-75)/(-21))*(-63)/(-72). Factor -3/2*i**4 - z*i**2 + 3/4 + 3/4*i - 15/4*i**3.
-3*(i + 1)**3*(2*i - 1)/4
Let o = 1958815/314811 + 1/34979. Solve -10/9*j**3 - o*j + 44/9*j**2 + 16/9 = 0.
2/5, 2
Let o(x) be the first derivative of -x**6/3 + 12*x**5/5 - x**4 - 40*x**3/3 + 27*x**2 - 20*x - 205. Suppose o(h) = 0. What is h?
-2, 1, 5
Let h(n) be the third derivative of -8/9*n**3 - 1/90*n**6 + 0 + 0*n + 0*n**4 - 1/210*n**7 - 15*n**2 + 1/1008*n**8 + 4/45*n**5. Solve h(x) = 0 for x.
-2, -1, 2
Let h(u) be the second derivative of u**7/42 - u**6/150 - u**5/4 + u**4/12 + 2*u**3/3 - 2*u**2/5 - 284*u. Determine b, given that h(b) = 0.
-2, -1, 1/5, 1, 2
Let n(a) = -17*a**2 - 18*a + 62. Let u(c) = -5*c**2 - 6*c + 20. Let m(w) = 2*n(w) - 7*u(w). Let m(l) = 0. What is l?
-8, 2
Let r(t) = 8*t**2 + 64*t + 22. Let a(w) = -4*w**2 - 32*w - 12. Let s(p) = -11*a(p) - 6*r(p). Let s(y) = 0. Calculate y.
-8, 0
Let t(n) = n**2 - n. Let c(m) = -6*m**5 + 4*m**4 + 2*m**3 + 6*m**2 - 6*m. Let z(o) = 2*c(o) - 12*t(o). Determine q so that z(q) = 0.
-1/3, 0, 1
Let h(m) be the first derivative of -18*m**3/11 + 60*m**2/11 - 24*m/11 - 217. Factor h(r).
-6*(r - 2)*(9*r - 2)/11
Factor -42*c + 153 + 33*c**2 - 11*c**2 - 25*c**2.
-3*(c - 3)*(c + 17)
Let r(c) = -c**5 + c**4 - c**3 - c**2. Suppose 5*i = 14 - 4. Let m(y) = y**