. Let j be g(39). Let b(y) be the first derivative of 0*y + 1/6*y**j + 0*y**2 + 4/9*y**3 + 1. Factor b(v).
2*v**2*(v + 2)/3
Suppose -5*b = 3*p + 29, 5*b - p + 2*p = -23. Let m be (6/b)/(6/(-12)). Factor -3*k**m + 8 + 4*k - k**3 + 1 - 1 - 8*k**2.
-4*(k - 1)*(k + 1)*(k + 2)
Let y(x) = -2*x + 22. Let r be y(10). Factor -14*q**2 + 19*q**r + 45 + 17*q + 13*q.
5*(q + 3)**2
Factor -12*q**3 - 5*q**4 + 17*q**4 + 32*q**5 - 36*q**5 + 4*q**2.
-4*q**2*(q - 1)**3
Let a(k) be the first derivative of -3*k**5/25 + 39*k**4/5 - 1014*k**3/5 + 13182*k**2/5 - 85683*k/5 - 40. Factor a(g).
-3*(g - 13)**4/5
Let p = 6900/5383 + 3/769. Factor 0 + p*z**4 + 3/7*z**2 + 3/7*z**5 + 9/7*z**3 + 0*z.
3*z**2*(z + 1)**3/7
Suppose 25 - 21 = 2*b. Let 4*g**b - 12*g - 29 + 15 + 14 = 0. Calculate g.
0, 3
Let v be ((-336)/3528)/((-24)/21 + 1). Factor 0 + 2/3*g**4 + v*g**5 + 0*g**2 + 0*g - 4/3*g**3.
2*g**3*(g - 1)*(g + 2)/3
Find u, given that 1/6*u**4 + 3/2 + 0*u + 0*u**3 - 5/3*u**2 = 0.
-3, -1, 1, 3
Factor 86*h**2 + 50*h**3 - 95*h**3 + 130*h**2 + 48*h**3.
3*h**2*(h + 72)
Let k(s) be the third derivative of -1/48*s**6 + 0*s - 1/420*s**7 + 0 + 0*s**3 - 7/120*s**5 - 1/16*s**4 - 35*s**2. Factor k(h).
-h*(h + 1)**2*(h + 3)/2
Let b(u) be the first derivative of -u**3 - 414*u**2 - 57132*u - 96. Factor b(t).
-3*(t + 138)**2
Let m(o) be the second derivative of o**6/120 + o**5/4 + 13*o**4/8 - 55*o**3/6 + 121*o**2/8 + 4*o + 3. Suppose m(n) = 0. What is n?
-11, 1
Let z(k) = -6*k**4 - 2*k**3 + 4*k**2 + 4. Let p(f) = 7*f**4 + 3*f**3 - 4*f**2 - 5. Let m(h) = -4*p(h) - 5*z(h). Factor m(g).
2*g**2*(g - 2)*(g + 1)
Let s = -16 - -18. Let o(z) = -4*z - 33 + 0*z + 35 + 2*z**s. Let j(b) = b - 1. Let y(p) = 2*j(p) + o(p). Factor y(t).
2*t*(t - 1)
Let h(m) = 8*m**2 - 6*m - 6. Let n(g) = -g**2 + g - 1. Let x(f) = 11*f**2 - 8*f - 19. Let l(o) = 6*n(o) - x(o). Let a(d) = 13*h(d) + 6*l(d). Solve a(w) = 0.
-3, 0
Let o(v) be the third derivative of v**8/2016 + 11*v**7/1260 + 7*v**6/144 + 5*v**5/72 + 147*v**2. Suppose o(q) = 0. What is q?
-5, -1, 0
Let y(i) be the first derivative of -2*i**3/3 + 18*i**2 + 38*i + 39. Factor y(z).
-2*(z - 19)*(z + 1)
Let z(y) = 2*y**2 + 4*y - 1. Let s(u) = -3*u**2 - 23*u + 46. Let m(h) = -3*s(h) - 6*z(h). Determine g so that m(g) = 0.
4, 11
Let g = -32/15 - -136/45. Factor -g*c**2 + 2/3*c**3 + 2/9*c + 0.
2*c*(c - 1)*(3*c - 1)/9
Suppose 1/6*u + 1/2*u**3 + 1/6*u**4 + 0 + 1/2*u**2 = 0. What is u?
-1, 0
Let j(z) = 2*z**4 - z**3 - z**2 + 2*z. Let q(a) = 2*a**5 + 16*a**4 - 9*a**3 - 29*a**2 + 26*a. Let n(w) = -6*j(w) + 2*q(w). Factor n(k).
4*k*(k - 1)**2*(k + 2)*(k + 5)
Let o(d) be the first derivative of -d**7/42 + d**6/15 + d**5/20 - d**4/6 + 2*d - 11. Let v(a) be the first derivative of o(a). Factor v(t).
-t**2*(t - 2)*(t - 1)*(t + 1)
Let s = -1007/203 + 148/29. Factor -3/7*p + s - 4/7*p**2.
-(p + 1)*(4*p - 1)/7
Let k(r) be the second derivative of 2*r**6/15 + 2*r**5/5 - 7*r**4/3 - 16*r**3/3 + 24*r**2 + 278*r. Suppose k(z) = 0. Calculate z.
-3, -2, 1, 2
Let v(p) = -2*p + 33. Let m be v(14). Factor -2 - 3*i + i**5 - 2*i**2 + 4*i**4 + 13*i - 4*i**3 - m*i - 2*i**5.
-(i - 2)*(i - 1)**3*(i + 1)
Let k = 112/1065 + 2/71. Let u(c) be the first derivative of k*c**3 + 1/10*c**4 - 2/5*c**2 + 0*c + 11. Factor u(n).
2*n*(n - 1)*(n + 2)/5
Let t be (-22)/(-46)*77/(-14). Let m = -3/23 - t. Factor m*d - 5*d**2 + 0 + 5/2*d**3.
5*d*(d - 1)**2/2
Let a(n) be the second derivative of n**4/12 + n**3/6 + n**2/2 - 20*n. Let l = -2 - -3. Let c(s) = -s + 1. Let k(d) = l*c(d) - a(d). Solve k(b) = 0 for b.
-2, 0
Let i(p) be the third derivative of p**6/90 - p**5/6 - p**4 + 11*p**3/6 + 17*p**2. Let n(d) be the first derivative of i(d). Suppose n(t) = 0. Calculate t.
-1, 6
Suppose 40 = -27*y + 37*y. Let j(f) be the second derivative of y*f + 0*f**3 - 1/60*f**5 + 0*f**2 + 1/18*f**4 + 0. Factor j(m).
-m**2*(m - 2)/3
Let d be 2/8 - (2 - (-1329)/(-12)). Factor 114*q**2 - d*q**2 + 8*q**5 + 9*q**4 - 3*q**5 - 14*q**4 - 5*q**3.
5*q**2*(q - 1)**2*(q + 1)
Let a(t) be the third derivative of -2*t**7/315 + 2*t**6/45 - t**5/15 - 10*t**2. Factor a(d).
-4*d**2*(d - 3)*(d - 1)/3
Let q be (-1 - -1) + (-2)/(-2) + 0. Suppose 10*b**2 - 5 + 3*b**3 - 8*b - q + b**3 = 0. Calculate b.
-3, -1/2, 1
Factor -24*q**2 - 44/7*q**3 + 0 + 24/7*q**4 - 2/7*q**5 - 14*q.
-2*q*(q - 7)**2*(q + 1)**2/7
Let m(i) = -i**3 - i**2 + i + 1. Let f be m(-1). Let n(x) = x**2 + 7*x - 17. Let d be n(-9). Factor -d + 2*u + 14*u**4 - 13*u**4 + f - 2*u**3.
(u - 1)**3*(u + 1)
Let j be (-2)/(-9)*(-87)/(-580). Let d(o) be the second derivative of -o + 0 - 2/5*o**2 + 1/25*o**5 - 1/3*o**3 - j*o**4. Factor d(a).
2*(a - 2)*(a + 1)*(2*a + 1)/5
Factor -20 + 35*x**3 + 4*x - 38*x**2 - 5*x**4 + 61*x - 17*x**2 - 20*x**2.
-5*(x - 4)*(x - 1)**3
Let o = -6 + 20. Let z = -9 + o. Factor -77*b**3 + 2*b**z - 5*b**4 + 85*b**3 + 13*b**4.
2*b**3*(b + 2)**2
Let n(c) be the first derivative of 0*c + 145/4*c**4 - 10*c**2 - 6 + 40/3*c**3 + 12*c**5. Solve n(t) = 0.
-2, -2/3, 0, 1/4
Let i(l) be the second derivative of 0*l**3 + 0*l**2 + 0 - 1/168*l**7 - 3/20*l**5 + 6*l + 1/20*l**6 + 1/6*l**4. Determine h, given that i(h) = 0.
0, 2
Let w(l) = -l**2 - 9*l - 8. Let p(t) = -t**2 - 10*t - 9. Let j be (-6)/8*6*16/12. Let v(f) = j*w(f) + 5*p(f). Determine a, given that v(a) = 0.
-3, -1
Let z = 8690 + -8688. Solve -1/4*n**3 + 3/2*n**2 - 3*n + z = 0.
2
Let x = -144/89 - -3804/1691. Determine s, given that 0 + 2/19*s**3 + x*s**2 + 10/19*s = 0.
-5, -1, 0
Suppose 231*m + 60 = 243*m. Let c(t) be the third derivative of -7*t**2 + 0*t - 1/24*t**4 + 1/60*t**m + 0*t**3 + 0. Determine o, given that c(o) = 0.
0, 1
Let t(w) = -296*w - 11838. Let i be t(-40). Factor 2/7*d + 0 - 2/7*d**3 + 0*d**i.
-2*d*(d - 1)*(d + 1)/7
Factor 45*d**2 + 54*d + 12*d**3 - 297*d**4 + 155*d**4 + 143*d**4.
d*(d + 3)**2*(d + 6)
Suppose 4*u + 50 = 2*m, -3*m - 5*u = -5*m + 50. Let f be m/12 - (-8)/(-24). What is n in 1/4 - 25/4*n**3 + 19/4*n**2 + 4*n**4 - n**5 - f*n = 0?
1/2, 1
Let c(q) be the first derivative of -2*q**3/3 + 103*q**2/5 + 84*q/5 - 70. Let c(h) = 0. What is h?
-2/5, 21
Suppose 34*z**2 + 40*z**2 - 110*z**2 + 162*z + 2*z**3 = 0. What is z?
0, 9
Let v(j) = j + 22. Let p be v(-20). Solve -14*t + 40*t**2 - 32*t**p - 4*t**4 - 4 + t**3 - 14*t**5 + 27*t**3 = 0 for t.
-1, -2/7, 1
Find w such that -26/5*w**2 + 36/5 - 2/5*w**4 + 14/5*w**3 - 6/5*w = 0.
-1, 2, 3
Let o(b) be the third derivative of -b**7/3780 + b**6/540 - b**4/2 - 14*b**2. Let a(x) be the second derivative of o(x). Factor a(l).
-2*l*(l - 2)/3
Suppose -5*v + r = -3*r - 20, 0 = -r. Suppose -5*f + v = -6. Factor f*i**3 + 2*i - 3*i**3 + 2*i - 3*i**3.
-4*i*(i - 1)*(i + 1)
Let a(w) = -16*w**3 - 52*w**2 - 63*w - 13. Let y(m) = 11*m**3 + 35*m**2 + 42*m + 8. Let v(d) = -5*a(d) - 7*y(d). Factor v(c).
3*(c + 1)**2*(c + 3)
Let g(v) be the first derivative of -25921*v**3/6 + 161*v**2 - 2*v + 446. Factor g(f).
-(161*f - 2)**2/2
Let k = 374 - 671. Let n = -297 - k. Factor n + 0*h - 12/7*h**3 + 12/7*h**2 + 3/7*h**4.
3*h**2*(h - 2)**2/7
Let p = 14 - 11. Factor -10*f**2 + 24*f**2 - 12*f**2 - f**5 + p*f**3.
-f**2*(f - 2)*(f + 1)**2
Find a such that 4*a**2 + 370*a + 431*a + 40804 + 7*a = 0.
-101
Let q(j) = 2*j**4 - 29*j**3 + 6*j**2 - 4. Let c(p) = -30*p**3 + 5*p**2 - 5. Let o(x) = 4*c(x) - 5*q(x). Suppose o(k) = 0. What is k?
0, 1/2, 2
Solve 0 + 2/13*o**3 - 10/13*o**2 + 8/13*o = 0 for o.
0, 1, 4
Suppose 1/4*j - 1/4*j**2 + 3 = 0. Calculate j.
-3, 4
Let t(z) = 2*z**3 + 243*z**2 - 20172*z + 551365. Let y(j) = 3*j**3 + 487*j**2 - 40344*j + 1102731. Let s(i) = -5*t(i) + 3*y(i). Factor s(a).
-(a - 82)**3
Factor -48/13*m + 46/13*m**2 + 0 + 2/13*m**3.
2*m*(m - 1)*(m + 24)/13
Let b(h) be the first derivative of 1/3*h**3 - 7/24*h**4 - 2 + 0*h + 1/12*h**5 + 2*h**2. Let n(k) be the second derivative of b(k). Factor n(j).
(j - 1)*(5*j - 2)
Let g(c) = -2*c - 2*c - 1 - 2*c - 2. Let m be g(-1). Determine r so that -3*r - 3*r**m - 4*r**2 - r**2 - r**2 = 0.
-1, 0
Let w(g) be the first derivative of g**7/4620 - g**6/132 + 5*g**5/44 - 125*g**4/132 - 10*g**3/3 - 21. Let t(z) be the third derivative of w(z). Factor t(i).
2*(i - 5)**3/11
Factor -1/4*g**3 + 2 - 1/2*g - 5/4*g**2.
-(g - 1)*(g + 2)*(g + 4)/4
Let j = 49 + 4. Let i = -49 + j. What is n in -51/5*n - 24/5*n**3 + 48/5*n**i - 6/5 - 117/5*n**2 = 0?
-1, -1/4, 