**4 - 8*a**2 - 6*a - 5. Let s be (-3 - (3 - 5) - -7)/2. Let r(h) = -7*h**2 - 5*h - 6. Let o(z) = s*r(z) - 4*f(z). Factor o(y).
-(y - 2)*(y + 1)*(2*y + 1)**2
Let p be 4/(-5)*(27 + -28). Let b = 4 - 4. Factor 2/5*g**4 + b + 0*g**3 - 6/5*g**2 - p*g.
2*g*(g - 2)*(g + 1)**2/5
Let w be 10 + 3/12*0. Let h be (-18)/w + (6 - (-24)/(-8)). Factor 3/5*o**4 + 3/5*o**2 - 9/5*o**3 + 9/5*o - h.
3*(o - 2)*(o - 1)**2*(o + 1)/5
Let p(q) = q**2 - 8*q + 6. Let j be p(8). Let r(u) be the first derivative of 1 + 0*u + 0*u**2 - 1/12*u**4 + 1/18*u**j + 0*u**5 + 0*u**3. What is a in r(a) = 0?
-1, 0, 1
Let z = -613/42 - -310/21. Factor 3/2 + z*k**2 + k.
(k + 3)**2/6
Let u(f) = -2*f + 5. Let t be u(0). Factor -3*a**2 + 12*a**2 - 4*a**2 - t.
5*(a - 1)*(a + 1)
Find t, given that -t**3 + 0*t**2 + 0*t**4 + 1/5*t**5 + 0 + 4/5*t = 0.
-2, -1, 0, 1, 2
Let x(g) be the second derivative of -g**5/8 + 3*g**4/16 + 19*g**3/24 + 3*g**2/4 - 2*g + 3. Find a such that x(a) = 0.
-3/5, -1/2, 2
Factor 3/2*f**4 - 3/4 + 3/8*f**5 + 3/2*f**3 - 3/4*f**2 - 15/8*f.
3*(f - 1)*(f + 1)**3*(f + 2)/8
Suppose 280*l = 109*l + 342. Factor 3/5*z**l + 3/5*z - 18/5.
3*(z - 2)*(z + 3)/5
Let g(x) be the third derivative of 1/630*x**7 - 7*x**2 - 2/9*x**3 - 1/90*x**6 + 1/60*x**5 + 1/18*x**4 + 0 + 0*x. Factor g(s).
(s - 2)**2*(s - 1)*(s + 1)/3
Let r = 94 - 69. Solve 51*z + 5*z**2 - 27*z - 1 - 3*z**3 - r*z = 0 for z.
-1/3, 1
Let s(w) be the third derivative of -w**5/210 - 5*w**4/28 - 919*w**2. Factor s(m).
-2*m*(m + 15)/7
Solve -2*c - 130 - 8*c**2 + 130 - 6*c**3 = 0 for c.
-1, -1/3, 0
Suppose -4*k + 2*p + 2 = -6, 4 = 5*k - p. Factor k - 4*g + 3*g**2 - 12 + 6 + 7*g.
3*(g - 1)*(g + 2)
Factor -8*m + 30*m**3 - 5*m**5 - 29*m**2 + 23*m - 24*m**2 + 13*m**2.
-5*m*(m - 1)**3*(m + 3)
Let r(o) = o**2 - 34*o - 80. Let a(s) = -2*s**2 + 33*s + 80. Let n(u) = 4*a(u) + 3*r(u). Suppose n(j) = 0. Calculate j.
-2, 8
Let p(v) be the first derivative of -v**4/2 + 4*v**3/3 + 3*v**2 + 55. Factor p(x).
-2*x*(x - 3)*(x + 1)
Let j be (8/(-6))/((-8)/24). Let s(c) be the first derivative of 4/21*c**3 + 0*c - 4 + 0*c**2 - 1/2*c**j. Suppose s(v) = 0. Calculate v.
0, 2/7
Let m(k) = k**2 + 5*k + 4. Let d be m(-4). Let l(j) be the second derivative of 0*j**3 + d + 0*j**2 + 1/24*j**4 - 2*j. Factor l(x).
x**2/2
Let t(r) be the second derivative of -1/5*r**5 - 1 + 25*r - 12*r**2 + 2/3*r**4 + 10/3*r**3. Factor t(c).
-4*(c - 3)*(c - 1)*(c + 2)
Let o(v) be the first derivative of -2*v**5/15 - 2*v**4/3 + 4*v**3/3 + 4*v**2/3 - 10*v/3 - 582. Find g such that o(g) = 0.
-5, -1, 1
Let l(w) be the third derivative of -5*w**8/336 + w**7/21 + w**6/6 - 2*w**5/3 + 59*w**2. Find v such that l(v) = 0.
-2, 0, 2
Let p(b) be the third derivative of -1/18*b**4 + 0 + 1/180*b**5 + 0*b + 0*b**3 - 8*b**2. Factor p(j).
j*(j - 4)/3
Let g = -39 - -62. Let k be (-1)/(-6) - (2 + g/(-6)). Determine i so that -i**3 + 3*i**4 + 1/2 - 7/2*i**k - 3/4*i + 7/4*i**5 = 0.
-1, 2/7, 1
Let w(u) = 16*u**4 - 21*u**3 - 34*u**2 + 18*u + 15. Let r(h) = 48*h**4 - 64*h**3 - 101*h**2 + 55*h + 46. Let o(j) = -3*r(j) + 8*w(j). Factor o(z).
-(z - 2)*(z - 1)*(4*z + 3)**2
Let z(b) = -5*b**5 + 11*b**4 - 5*b**3 - 3*b**2 + 6*b + 4. Let j(l) = 10*l**5 - 21*l**4 + 8*l**3 + 7*l**2 - 11*l - 7. Let x(q) = 4*j(q) + 7*z(q). Factor x(a).
a*(a - 1)**2*(a + 1)*(5*a - 2)
Let m(v) be the first derivative of v**5/15 - v**4/12 + 17*v**2 - 10. Let x(j) be the second derivative of m(j). Factor x(l).
2*l*(2*l - 1)
Let a(i) = -2*i**2 + 39*i**5 - i**3 + 3*i**2 - 38*i**5. Let x(j) = -16*j**4 + 34*j**3 - 2*j**2. Let z(u) = 2*a(u) + x(u). Find f such that z(f) = 0.
0, 4
Factor 0 + n - 16*n**2 + 31*n + 0 + 2*n**3.
2*n*(n - 4)**2
Let v(b) = 5*b**3 + b**2 - 2. Let k be v(1). Suppose -2*m + 5 = -3*q + 1, 4*q + 8 = k*m. Factor -8/9*j**m - 2/3*j + 2/9.
-2*(j + 1)*(4*j - 1)/9
Suppose -5*s = 7 - 27. Suppose 2*l - s = 12. Factor -5*i**2 + l*i - 2*i + 2*i**2.
-3*i*(i - 2)
Let j = -23 + 23. Suppose 13*a - 9*a = j. Factor 2/7*m + a - 2/7*m**2.
-2*m*(m - 1)/7
Let t = 13 - -38. Let 0 + t + 5*f**2 + 30*f - 6 = 0. Calculate f.
-3
Let i = -150 + 152. Let 2*r**3 + 10/3*r**i + 4/3*r + 0 = 0. Calculate r.
-1, -2/3, 0
Let z(i) be the third derivative of i**8/504 - i**7/105 + 2*i**5/45 + 62*i**2. Factor z(m).
2*m**2*(m - 2)**2*(m + 1)/3
Determine p so that -1280*p**5 - 10514*p**2 - 27 - 1566*p**2 - 98 - 22399*p**4 - 32480*p**3 - 2005*p - 10881*p**4 = 0.
-25, -1/4
Factor -1890*c**5 - 20*c**4 - 3*c**3 - 22*c**3 - 10*c**2 + 1885*c**5.
-5*c**2*(c + 1)**2*(c + 2)
Let q(r) be the first derivative of r**6/2 - 18*r**5/5 - 3*r**4/4 + 38*r**3 - 96*r - 44. Suppose q(s) = 0. Calculate s.
-2, -1, 1, 4
Let b be 168/112 + (1/(-1) - 20/(-8)). Factor -1/4*o**4 + 0 + 1/4*o**2 - 1/2*o + 1/2*o**b.
-o*(o - 2)*(o - 1)*(o + 1)/4
Let x(d) be the second derivative of 2*d**7/147 + 4*d**6/105 - 3*d**5/5 + 22*d**4/21 + 40*d**3/21 - 48*d**2/7 - 53*d. Suppose x(h) = 0. What is h?
-6, -1, 1, 2
Let f(k) be the second derivative of 7*k**6/60 + 6*k**5/5 + 83*k**4/24 - 7*k**3/2 - 36*k**2 - 2*k + 268. Solve f(b) = 0 for b.
-3, -2, 8/7
Let v(o) be the third derivative of -o**5/420 + 11*o**4/168 + 13*o**3/21 + 2*o**2 - 20*o. Determine g so that v(g) = 0.
-2, 13
Let s be (-8)/(-68) - 198/(-51). Factor -16*w**3 + 15*w**4 - 36*w**2 - 17*w**s - 36*w - 23*w**2 + 17*w**2.
-2*w*(w + 2)*(w + 3)**2
Factor 14 + 1/3*c**2 + 23/3*c.
(c + 2)*(c + 21)/3
Let d = -62 + 56. Let z(v) = -v**4 + 7*v**3 + 2*v**2 + 7*v - 8. Let f(y) = -y**4 + 6*y**3 + 2*y**2 + 6*y - 7. Let k(m) = d*z(m) + 7*f(m). Factor k(t).
-(t - 1)**2*(t + 1)**2
Let y(k) be the third derivative of -k**6/60 - 47*k**5/90 - 3*k**4 - 52*k**3/9 - 604*k**2. Determine v so that y(v) = 0.
-13, -2, -2/3
Factor -1/6*w**5 + 4/3*w - w**3 - 5/6*w**4 + 2/3*w**2 + 0.
-w*(w - 1)*(w + 2)**3/6
Let f(d) = 10*d**2 - 117*d + 49. Let j(p) = -11*p**2 + 113*p - 48. Let v(x) = -6*f(x) - 5*j(x). Solve v(k) = 0 for k.
2/5, 27
Let c be (-4)/28*(-78)/3. Determine g, given that 2/7*g - c*g**4 + 8/7*g**5 + 30/7*g**3 + 0 - 2*g**2 = 0.
0, 1/4, 1
Determine b, given that -b**2 + 2/3*b + 1/3*b**3 + 0 = 0.
0, 1, 2
Let q(v) be the third derivative of 29*v**5/60 - 43*v**4/6 - 2*v**3 - 14*v**2 + 8*v. Suppose q(p) = 0. Calculate p.
-2/29, 6
Let j be (-35)/(-21)*(-41)/(-410). Determine t so that 1/3 - j*t**3 + 2/3*t**2 - 5/6*t = 0.
1, 2
Let w(m) be the first derivative of -m**6/180 - m**5/20 - m**4/6 - 10*m**3/3 - 11. Let d(v) be the third derivative of w(v). Determine l so that d(l) = 0.
-2, -1
Let 866*l**2 + 263*l - 27*l - 32*l - 894*l**2 - 56 = 0. Calculate l.
2/7, 7
Let f(c) be the third derivative of c**7/105 + c**6/30 + c**5/30 + 18*c**2. What is l in f(l) = 0?
-1, 0
Determine b so that 4/3 + 3*b + 2*b**2 + 1/3*b**3 = 0.
-4, -1
Let j(m) be the first derivative of 6 - 12*m**3 - 6*m**2 - 6/5*m**5 - 27/4*m**4 + 0*m. Factor j(t).
-3*t*(t + 2)**2*(2*t + 1)
Suppose 5*p - 15 = 5*j, 4*p + 17 = 3*j + 26. Factor 0 + 4/11*b**4 + 2/11*b**3 + 2/11*b**5 + p*b + 0*b**2.
2*b**3*(b + 1)**2/11
Let q = 710/1119 - -12/373. Let n(f) be the first derivative of 0*f - 9 - q*f**3 + 1/12*f**4 + 3/2*f**2. Solve n(l) = 0.
0, 3
Let x be ((-2622)/21413)/(2/(-14)). Factor 2/7*b**2 + 0 - x*b.
2*b*(b - 3)/7
Let z(n) be the second derivative of -n**7/21 - 2*n**6/105 + n**5/10 + n**4/21 + 46*n. Find w such that z(w) = 0.
-1, -2/7, 0, 1
Let u(x) = -x**2 - 39*x - 106. Let g be u(-36). Determine j, given that 6/5 - 8/5*j + 2/5*j**g = 0.
1, 3
Let y(v) be the first derivative of v**4/38 + 2*v**3/57 - 6*v**2/19 + 256. Solve y(r) = 0.
-3, 0, 2
Let h(n) = 13*n**2 - 336*n - 349. Let p(s) = -11*s**2 + 337*s + 348. Let m(o) = -3*h(o) - 4*p(o). Factor m(c).
5*(c - 69)*(c + 1)
Let l(k) be the first derivative of k**5/5 - 39*k**4/4 + 25*k**3 - 37*k**2/2 - 460. Solve l(j) = 0 for j.
0, 1, 37
Suppose 6 = 4*z - 2. Suppose -z*d = 10, 0*d = -4*p + d + 41. Determine f, given that p*f - 3*f**4 - 3*f + 6*f**4 - 6*f**3 - 3*f**2 = 0.
-1, 0, 1, 2
Let j(g) be the third derivative of -g**7/35 - g**6/24 + 7*g**5/60 + 5*g**4/24 - g**3/6 - 49*g**2. Factor j(y).
-(y - 1)*(y + 1)**2*(6*y - 1)
Suppose 2*p - 72 = -16*p. Let m(j) be the second derivative of -5/27*j**3 + 1/90*j**5 - 1/3*j**2 - 1/54*j**p + 0 + 4*j. Factor m(z).
2*(z - 3)*(z + 1)**2/9
Let b(h) be the second derivative of -h**6/75 + 11*h**5/50 - 19*h**4/30 + 3*h**3/5 - 29*h - 