)*0. Let p = -44/65 - -14/13. Factor -2/5*x**4 + 0*x + g - p*x**2 - 4/5*x**3.
-2*x**2*(x + 1)**2/5
Find f, given that 83*f**2 - 244*f**2 + 78*f**2 - 512 + 87*f**2 + 112*f = 0.
-32, 4
Let g(p) = p**3 - p + 1. Let d(i) = -4*i**3 + 6*i**2 - 2*i - 3. Let h(x) = d(x) + 3*g(x). Factor h(u).
-u*(u - 5)*(u - 1)
Factor 2*g + 3*g**4 + g + 9*g**3 + 56*g**2 - 47*g**2.
3*g*(g + 1)**3
Let h(p) be the first derivative of 5*p**6/14 + 54*p**5/35 - 39*p**4/14 - 96*p**3/7 + 135*p**2/14 + 162*p/7 + 246. Let h(r) = 0. Calculate r.
-3, -3/5, 1, 2
Let c(g) be the third derivative of g**6/120 - g**5/12 + g**4/6 - 65*g**2 + 2*g. Factor c(u).
u*(u - 4)*(u - 1)
Factor 3*f**2 + 7867 + 7*f + 27125 - 281*f - 374*f.
3*(f - 108)**2
Let y(b) be the second derivative of -b**5/130 + 11*b**4/78 - 31*b**3/39 + 21*b**2/13 + 312*b. Factor y(w).
-2*(w - 7)*(w - 3)*(w - 1)/13
Suppose 4*j = k + 22, j = -3*k - 3 + 2. Let f(z) = -3*z - 4. Let o be f(k). Solve -3*m**2 + 5*m**o - 2*m**2 + 3*m**3 + 6*m**4 = 0 for m.
-1/2, 0
Let a be 8/28 + (-124)/(-7). Let b = -16 + a. Factor -8 + 51*d**2 + 3*d**b + 52*d**3 + 5*d + 19*d**4 + 3*d - 5*d**4.
2*(d + 1)**2*(d + 2)*(7*d - 2)
Let l = 226/19 + -81341/6840. Let p(y) be the third derivative of 5*y**2 + 1/180*y**5 + 0 - l*y**6 + 0*y**3 + 0*y + 0*y**4. Let p(g) = 0. What is g?
0, 1
Suppose -71*x = -22*x - 147. Let o(b) be the second derivative of -1/10*b**5 + 8*b + 2/3*b**4 + 0 - b**x + 0*b**2. Determine l so that o(l) = 0.
0, 1, 3
Let j be ((-5)/(-20) + -4)*80/(-6). Let r be -1*j/(-56) + 9/36. Find a, given that -18/7*a**2 + 40/7*a - r = 0.
2/9, 2
Let v = 10 - 6. Suppose 0 = 2*z + v*k - 20, 0 = 3*z + 4*k - 4 - 18. Factor w - 2*w**2 + 3*w**2 + w**z - w**2.
w*(w + 1)
Suppose 9*m**2 + 2*m**4 - 2744 + 21*m**2 - 14*m**3 + 2752 - 26*m = 0. What is m?
1, 4
Let j(d) be the second derivative of 1/42*d**4 + 0*d**3 + 0*d**2 + 14*d + 0 - 1/70*d**5. Determine y, given that j(y) = 0.
0, 1
Let l(b) be the first derivative of -2*b**5/15 - 2*b**4 + 2*b**3/3 + 34*b**2/3 - 16*b + 33. Solve l(z) = 0.
-12, -2, 1
Let q(n) be the third derivative of n**5/140 + n**4/8 + 5*n**3/7 - 2*n**2 + 5. Factor q(s).
3*(s + 2)*(s + 5)/7
Let x = -12 - -10. Let s(m) = m**3 - m**2 + m - 1. Let j(y) = y**3 - 3*y + 2. Let u(w) = x*s(w) - 2*j(w). Factor u(g).
-2*(g - 1)*(g + 1)*(2*g - 1)
Let n(i) = -3 - 5*i - 2*i**2 - 2*i + 24*i**3 - 25*i**3. Let l(c) = -3*c**3 - 8*c**2 - 29*c - 13. Let p(q) = -6*l(q) + 22*n(q). Factor p(g).
-4*(g - 3)*(g + 1)**2
Let z(v) be the second derivative of -5/4*v**4 + 0 + 9/4*v**3 - 9/4*v**2 + 1/252*v**7 - 11/180*v**6 + 23/60*v**5 - 10*v. Find d, given that z(d) = 0.
1, 3
Let v = 276/5 - 2203/40. Let z(d) be the third derivative of 7*d**2 + 3/4*d**3 + 0 - 1/40*d**5 + 0*d - v*d**4. What is r in z(r) = 0?
-3, 1
Let s = -4189 + 16757/4. Let 0 + 0*g + 1/2*g**2 + s*g**3 - 1/4*g**4 = 0. Calculate g.
-1, 0, 2
Let n(m) be the second derivative of 2/3*m**6 + 0*m**3 + 0 + 0*m**2 + 5/6*m**4 - 5/4*m**5 - 5/42*m**7 + 2*m. Factor n(u).
-5*u**2*(u - 2)*(u - 1)**2
Let s(j) be the first derivative of -1/12*j**4 + 1/2*j**2 + 2/3*j - 38 + 0*j**3. Suppose s(n) = 0. What is n?
-1, 2
Let v = 13 - 8. Suppose -2*m = -0 + 2, m + 11 = v*u. Factor 0 + 1/6*i + 1/6*i**5 + i**3 - 2/3*i**4 - 2/3*i**u.
i*(i - 1)**4/6
Suppose -2 = -3*r + 1. Find v, given that 2*v**2 + 2*v**4 + v**5 - v**3 - r - v**3 + v - 3*v**4 = 0.
-1, 1
Let s(i) be the first derivative of -i**4/84 - 5*i**3/42 + 3*i**2/7 - 20*i + 15. Let u(o) be the first derivative of s(o). Find q, given that u(q) = 0.
-6, 1
Determine r, given that -1/2*r**3 - 1 + 1/2*r + r**2 = 0.
-1, 1, 2
Suppose -9*f - 7 = -8*f - 2*h, 0 = 3*f - 2*h + 1. Suppose -4*a - 24 + 4 = 0, 4*a + 32 = 3*n. Find g such that 3/2*g - f + 33/2*g**2 + 33/2*g**3 + 9/2*g**n = 0.
-2, -1, 1/3
Suppose 5*h = h + 12. Let v = -49 - -51. Factor -2*d**3 + 2 - 3*d + h*d**2 - 4*d + d + 3*d**v.
-2*(d - 1)**3
Let t(j) = 5*j**5 - 7*j**4 + j**3 + 11*j**2 - 6*j. Let d(v) = -4*v**5 + 7*v**4 - 2*v**3 - 10*v**2 + 6*v. Let f(i) = -4*d(i) - 3*t(i). Solve f(s) = 0 for s.
-1, 0, 1, 6
Let n(u) = -10*u**2 - 8*u - 15. Let b(p) = -27*p**2 - 24*p - 44. Let x(r) = 3*b(r) - 8*n(r). Determine d, given that x(d) = 0.
-6, -2
Let g(t) be the first derivative of t**6/30 - 4*t**5/15 + t**4/2 - t**2/2 - 14. Let f(d) be the second derivative of g(d). Determine r so that f(r) = 0.
0, 1, 3
Let m = -264 + 264. Let p(w) be the third derivative of 1/84*w**4 + 0*w + m + 1/210*w**5 - 5*w**2 - 2/21*w**3. Factor p(d).
2*(d - 1)*(d + 2)/7
Suppose 0 = -5*q - 0*q + 20. Let l be 16/3*6/q. Let 14*s**3 + 4*s - 19*s**2 + l*s**2 + 29*s**2 = 0. Calculate s.
-1, -2/7, 0
Let o(s) be the first derivative of s**5/10 + s**4/24 - 4*s**3/3 - s**2 - 28*s + 31. Let u(g) be the first derivative of o(g). Factor u(t).
(t - 2)*(t + 2)*(4*t + 1)/2
Let x = 6/4985 + 29844/54835. Factor -2/11*r**3 - x*r**2 + 0*r + 8/11.
-2*(r - 1)*(r + 2)**2/11
Let o be 18/(-15)*((-250)/(-30) - 10). Solve -2/7*c**3 + 0 + 0*c**o + 2/7*c = 0.
-1, 0, 1
Let m(k) be the third derivative of -k**6/200 + k**5/30 + k**4/15 + 84*k**2. Find g, given that m(g) = 0.
-2/3, 0, 4
Suppose 0 = -3*l, 2*y - 4*l = 6*y - 20. Factor 11*f - y*f**3 + 7*f**4 - 6*f**2 - f**5 - f**2 - 9*f + 4*f.
-f*(f - 6)*(f - 1)**2*(f + 1)
Let -25 + 144/5*d**3 - 1296/5*d**4 + 152*d**2 - 864/5*d**5 + 10*d = 0. What is d?
-5/6, 1/2
Let x(u) be the second derivative of -u**4/18 + 3*u**3 - 26*u**2/3 - 254*u. Solve x(m) = 0 for m.
1, 26
Solve -12/7*p**2 + 2/7*p**3 + 0 + 18/7*p = 0 for p.
0, 3
Let 24/5*q**3 - 4/5*q**4 - 4/5*q**5 + 0*q**2 + 0*q + 0 = 0. Calculate q.
-3, 0, 2
Let b be ((-18)/(-27))/(2/30). Suppose 0 = -y + b. Factor 0*q**3 - 2*q**3 + y*q**4 - 8*q**4.
2*q**3*(q - 1)
Let h(r) = -10*r**4 + 110*r**3 - 406*r**2 + 324*r + 6. Let n(z) = -z**4 - z**3 + z**2 + 4*z + 1. Let b(l) = h(l) - 6*n(l). Let b(f) = 0. Calculate f.
0, 1, 3, 25
Let m(d) be the first derivative of d**3/6 - 29*d**2 + 1682*d + 818. Factor m(z).
(z - 58)**2/2
Let h(x) be the second derivative of 2*x**2 + 1/18*x**4 + 0 + 1/90*x**5 - 1/3*x**3 - x. Let q(w) be the first derivative of h(w). Factor q(k).
2*(k - 1)*(k + 3)/3
Let m(n) be the first derivative of 2*n**6/15 + n**5 + 7*n**4/3 + 2*n**3 - 33*n + 31. Let a(h) be the first derivative of m(h). Factor a(z).
4*z*(z + 1)**2*(z + 3)
Let -913066/5 + 35574/5*d - 462/5*d**2 + 2/5*d**3 = 0. Calculate d.
77
Let k(y) = -y**3 - y**2 + y. Let d(t) = -53*t**3 + 15*t**2 + 30*t - 1. Let s(l) = -4*d(l) + 36*k(l). Factor s(a).
4*(a - 1)*(2*a + 1)*(22*a - 1)
Let q be 10/8 - 9/12*-1. Let d(p) be the third derivative of -3/16*p**3 - 1/1680*p**7 + 1/16*p**4 + 1/240*p**5 - 1/240*p**6 + 0 - q*p**2 + 0*p. Factor d(s).
-(s - 1)**2*(s + 3)**2/8
Let f(n) = -n**2 + 8*n + 132. Let j be f(16). Find k, given that -4/7*k**2 - 4/7*k**3 + 4/7*k + 4/7*k**j + 0 = 0.
-1, 0, 1
Let t(x) be the first derivative of 2*x**5/5 + 4*x**4 - 2*x**3/3 - 8*x**2 + 1. Factor t(y).
2*y*(y - 1)*(y + 1)*(y + 8)
Suppose -12*c + 11*c = 0. Let p(m) be the second derivative of 1/60*m**6 + c*m**3 - 1/40*m**5 + 0 - 5*m + 0*m**4 + 0*m**2. Factor p(v).
v**3*(v - 1)/2
Let j(u) = -4*u**5 + 12*u**4 - 2*u**2 + 2*u + 2. Let h(s) = 17*s**5 - 49*s**4 + 9*s**2 - 9*s - 9. Let g(c) = 2*h(c) + 9*j(c). Factor g(z).
-2*z**4*(z - 5)
Let x(u) be the first derivative of 5*u**4/4 - 94*u**3/3 - 19*u**2/2 + 216. Determine s so that x(s) = 0.
-1/5, 0, 19
Let w(g) = -14*g - 610. Let r be w(-44). Let k(f) be the first derivative of -3 + 32/15*f**3 + 1/30*f**r + 8/5*f**2 + 6/5*f**4 + 0*f + 8/25*f**5. Factor k(l).
l*(l + 2)**4/5
Let i = 2/3957 - -11743/253248. Let y = 171/448 + i. Factor -9/7 - 6/7*t + y*t**2.
3*(t - 3)*(t + 1)/7
Let -32/9 - 124/9*y**3 + 124/9*y - 16/9*y**4 + 16/3*y**2 = 0. What is y?
-8, -1, 1/4, 1
Suppose 2 = 3*s - s, 0 = -3*b + 2*s + 7. Let d be (-18 + b)*3/(-9). Determine l so that 2*l - d*l**4 + 15*l**2 + 4*l - l - 10 - 5*l**3 = 0.
-2, -1, 1
Let c(r) be the third derivative of 2/15*r**3 + 1/15*r**4 + 0 - 34*r**2 + 0*r + 1/75*r**5. What is z in c(z) = 0?
-1
Let t = 859/2 - 439. Let i = t - -10. Factor 0*f + i*f**2 - 1/4*f**3 + 0.
-f**2*(f - 2)/4
Find a, given that 36*a**5 + 23*a**3 - 2*a**2 + 29*a**5 - 76*a + 4*a**4 + 32*a**5 + 25*a**5 - 56 - 123*a**5 = 0.
-2, -1, 2, 7
Let t(n) be the first derivative of n**6/12 + 19*n**5/10 + 79*n**4/8 - 119*n**