 = 37*d**2 + 15*d + 3. Let q(x) = -59*x**2 - 23*x - 4. Let i(t) = -8*f(t) - 5*q(t). Factor i(g).
-(g + 1)*(g + 4)
Suppose 355*t - 9 = 352*t. Find o such that -3/4*o**2 + 3/2*o**t + 0 + 0*o - 3/4*o**4 = 0.
0, 1
Let n(w) = -1. Let g(y) = 4*y**2 + 31*y - 2*y**2 + 30 + 2*y**2 - 7*y. Let j(a) = g(a) - 6*n(a). Let j(v) = 0. What is v?
-3
Let u(z) be the third derivative of -z**6/60 - 17*z**5/30 - 16*z**4/3 - 16*z**3 - 3*z**2 - 62*z. Factor u(b).
-2*(b + 1)*(b + 4)*(b + 12)
Let h(k) be the second derivative of 47/84*k**4 + 1/70*k**5 - 40*k - 72/7*k**2 + 0 + 44/7*k**3. Solve h(t) = 0 for t.
-12, 1/2
Factor -1/8*g**3 - 17/8*g + 5/4*g**2 + 1.
-(g - 8)*(g - 1)**2/8
Let q = 83/102 + -5/34. Factor -q*a**2 + 0 - 10/9*a.
-2*a*(3*a + 5)/9
Let f(j) = -j**3 - 6*j**2 + 8*j - 4. Let q be f(-7). Let g = q - -15. Determine i so that -19*i**3 + 5*i**g - 11*i**5 - 2*i**3 + 6*i**2 - 11*i**4 + 32*i**5 = 0.
-1, 0, 2/7, 1
Suppose 21*z = o + 19*z - 3, 0 = -4*o + 4*z + 8. Let c be (o + 2)*38/57. What is u in 1/2 - 1/4*u**c + 1/4*u = 0?
-1, 2
Let b(x) = -x**2 - 11*x - 15. Let c be b(-9). Suppose 66*g + 75*g**4 + 56 + 27*g**c - 47 + 12*g**5 + 135*g**3 + 156*g**2 = 0. Calculate g.
-3, -1, -1/4
Suppose -143 = -17*p + 4*p. Let s(d) = 50*d**2 - 31*d + 13. Let i(v) = -25*v**2 + 16*v - 7. Let j(c) = p*i(c) + 6*s(c). Factor j(k).
(5*k - 1)**2
Let t(q) be the first derivative of q**6/6 - 7*q**5/5 + 5*q**4/4 + 7*q**3/3 - 3*q**2 - 72. Factor t(n).
n*(n - 6)*(n - 1)**2*(n + 1)
Let a(f) = 2*f + 1. Let r be a(1). Suppose -31*n**3 + 8*n**2 - 23*n**3 + 52*n**r = 0. Calculate n.
0, 4
Let c(r) be the third derivative of 1/360*r**6 + 40*r**2 + 0*r + 0*r**3 + 0 + 0*r**4 + 1/180*r**5. Factor c(p).
p**2*(p + 1)/3
Let i(c) be the third derivative of 605*c**8/336 - 143*c**7/21 + 71*c**6/8 - 13*c**5/3 + 5*c**4/6 + 15*c**2 + 3*c. Factor i(o).
5*o*(o - 1)**2*(11*o - 2)**2
Let f(z) be the second derivative of z**6/30 + 2*z**5/5 + 7*z**4/4 + 11*z**3/3 + 4*z**2 + z - 118. What is h in f(h) = 0?
-4, -2, -1
Let g = 1293/2 + -646. Factor g*n + 0 + 5/4*n**2.
n*(5*n + 2)/4
Let v(l) be the first derivative of l**6/90 - l**4/12 + l**3/9 - 2*l + 11. Let z(s) be the first derivative of v(s). Factor z(o).
o*(o - 1)**2*(o + 2)/3
Let b = -17979/4 - -4495. Find a such that 0 + b*a**2 + 1/2*a = 0.
-2, 0
Let v(w) be the second derivative of -2*w**7/21 + 4*w**6/5 + 4*w**5/5 - 8*w**4 - 94*w. Solve v(y) = 0.
-2, 0, 2, 6
Let j(c) be the third derivative of -c**11/332640 + c**10/75600 - c**9/60480 + c**5/10 + 12*c**2. Let l(n) be the third derivative of j(n). Factor l(a).
-a**3*(a - 1)**2
Let k = -106 - -110. Suppose -4*q + 5*m + 20 = -q, 0 = -2*q - m - k. Determine p, given that -3/7*p**3 - 3/7*p**2 + 0 + q*p = 0.
-1, 0
Let b(y) be the second derivative of -y**9/11340 - y**8/1008 - 4*y**7/945 - y**6/135 - 13*y**4/4 + 6*y. Let j(t) be the third derivative of b(t). Factor j(i).
-4*i*(i + 1)*(i + 2)**2/3
Let x = 31623 + -31621. Find r, given that -192/5 - 3/5*r**x + 48/5*r = 0.
8
Factor -10/3*k**3 - 2/3*k**2 + 0 + 0*k - 3/2*k**4.
-k**2*(k + 2)*(9*k + 2)/6
Let h be (-4)/14*((-21)/12)/1. Solve 0*q**2 + 1 - 3/2*q + h*q**3 = 0.
-2, 1
Let b be (-1)/(((-2)/(-88))/((-2)/(-4))). Let q be 512/126 - b/99. What is d in -2/7 - 8/7*d**4 + 26/7*d**3 - q*d**2 + 2*d = 0?
1/4, 1
Let w(j) = 21*j**2 - 209*j - 90. Let k(c) = -16*c**2 + 210*c + 90. Let o(m) = 7*k(m) + 6*w(m). Factor o(z).
2*(z + 15)*(7*z + 3)
Let i(d) = d**2 - 1. Let v(a) = a**2 + 22*a - 22. Let k be v(-23). Let b(u) = -u**2 + 12*u + 13. Let y(c) = k*b(c) + 3*i(c). Suppose y(g) = 0. Calculate g.
-5, -1
Let s = 7659/68 - 1800/17. Let -3/2*n**2 - n**3 + 1/4*n**4 + 9*n - s = 0. What is n?
-3, 1, 3
Let x be (-8251)/(-37)*(-1 - -2). Let l = -1558/7 + x. Find g such that -l*g**2 - 6/7*g + 0 = 0.
-2, 0
What is g in -g**3 + 1/4*g**2 - 1 + 4*g = 0?
-2, 1/4, 2
Let n(k) = -k**3 + 9*k**2 + 14. Let c be n(10). Let v = 689/8 + c. Factor -1/8*t**2 + v*t - 1/8*t**3 + 1/8.
-(t - 1)*(t + 1)**2/8
Suppose 2*h - 9 = -p, -5*p + 9 = 4*h - 12. Suppose 14 + 66 = 10*n. Let 28*r**3 - 72*r + 20*r**3 + 17*r**4 - n*r**h - 27 + 42*r**2 = 0. Calculate r.
-3, -1/3, 1
Suppose 0 = 6*u - 63 - 27. Let g be 1*0/(u/(-3)). Determine v so that 2/7*v - 4/7*v**2 + 2/7*v**3 + g = 0.
0, 1
Let b = -525/2 + 263. Let r(f) be the second derivative of 0 + 4*f + 1/12*f**4 - b*f**2 - 1/4*f**3. Solve r(g) = 0.
-1/2, 2
Suppose z + 2 = 3*z. Let p be -1*z/6 - 111/(-370). Factor p*n**2 - 8/15*n + 2/5.
2*(n - 3)*(n - 1)/15
Let w(x) be the first derivative of 0*x - 1/20*x**5 + 2 - 1/2*x**4 - 2*x**3 - 2*x**2. Let m(s) be the second derivative of w(s). Factor m(h).
-3*(h + 2)**2
Let b(g) = 2*g**4 - 78*g**3 - 24*g**2 + 648*g + 856. Let h(j) = j**4 - 26*j**3 - 8*j**2 + 216*j + 285. Let v(k) = -3*b(k) + 8*h(k). Let v(w) = 0. Calculate w.
-12, -2, 3
Suppose -p = -0*p - 1, -y - 5*p = -6. Factor -8*r + y - 10 - 4*r - 3*r**2.
-3*(r + 1)*(r + 3)
Let o(y) = y + 9. Let v(c) = c + 10. Let q(a) = -2*o(a) + 3*v(a). Let h be q(-10). Solve 0 - 2/3*t**4 + h*t**2 - 4/3*t + 0*t**3 = 0.
-2, 0, 1
Let s be (4/54)/(3 - (-1681)/(-579)). Let h = s + -1/63. Solve 1/4*i**4 - 1/4*i - 3/4*i**3 + h*i**2 + 0 = 0.
0, 1
Factor -96/5*o + 24/5*o**3 + 4/5*o**2 + 4/5*o**4 + 64/5.
4*(o - 1)**2*(o + 4)**2/5
Suppose -3*a + 7 = -4*q, -2*q - 16 = -4*a - 0*q. Let b(j) = j - 3. Let r be b(a). Factor 46/7*f + 2*f**r + 12/7.
2*(f + 3)*(7*f + 2)/7
Determine y so that 52*y + 1848*y**2 - 4*y**3 + 11 - 1913*y**2 + 0 + 6 = 0.
-17, -1/4, 1
Let n = 106/137 - -354/959. Let 2/7*d**3 + 10/7*d + 4/7 + n*d**2 = 0. Calculate d.
-2, -1
Let h(o) = -6*o**4 + 46*o**3 + 54*o**2 + 16*o. Suppose -8 + 14 = -3*l. Let z(w) = -w**4 + w**3 - w. Let c(r) = l*z(r) - h(r). Solve c(b) = 0 for b.
-1/2, 0, 7
Let p(l) be the second derivative of 5*l**4/36 + 15*l**3 + 1215*l**2/2 - l + 6. Factor p(c).
5*(c + 27)**2/3
Let y(v) = -16*v**4 - 6*v**3 + 26*v**2 - 22*v + 4. Let o(i) = -i**4 - i**3 + i**2 - i + 1. Suppose 9*d - 29 + 11 = 0. Let m(s) = d*y(s) - 28*o(s). Factor m(k).
-4*(k - 5)*(k - 1)*(k + 1)**2
Let n = -168 + 162. Let i be (-15)/9 + (-2)/6*n. Let 0*j**2 + 0 + 0*j + i*j**3 - 1/3*j**4 = 0. Calculate j.
0, 1
Let n be (787/6 - 0)*(-76)/19. Let y = n + 532. Factor 4/3 + 2*k**4 + 6*k + 10*k**2 + y*k**3.
2*(k + 1)**3*(3*k + 2)/3
Let g(b) be the first derivative of 4*b**5/35 + 9*b**4/7 + 4*b**3 + 38*b**2/7 + 24*b/7 - 30. Factor g(k).
4*(k + 1)**3*(k + 6)/7
Suppose 4*p - 19 = 2*q - 3, 3*q + 8 = -2*p. Let -2/7*z**3 + 4/7*z**p + 0 - 2/7*z = 0. Calculate z.
0, 1
Let l be (9 - 9)/(1/1). Let c(v) be the third derivative of 0 + 1/90*v**5 + l*v**4 + 0*v**6 + 0*v - 4*v**2 - 1/630*v**7 - 1/18*v**3. Factor c(j).
-(j - 1)**2*(j + 1)**2/3
Let v(x) be the third derivative of -x**5/75 - x**4/15 + 2*x**3/5 - 105*x**2. Factor v(n).
-4*(n - 1)*(n + 3)/5
Let z(r) be the second derivative of -r**4/30 + 14*r**3/3 - 69*r**2/5 + 207*r. Factor z(a).
-2*(a - 69)*(a - 1)/5
Determine z, given that -3/2*z**3 + 12 - 9/2*z**2 + 9*z = 0.
-4, -1, 2
Let q be ((-85)/(-425))/((2 - 4) + 3). Let l(k) be the first derivative of -1/10*k**4 - q*k**2 - 4/15*k**3 + 0*k - 8. Solve l(j) = 0.
-1, 0
Suppose -26 - 5 = -5*g - 4*v, -5*g = 3*v - 27. Let n be ((g - 8)*15/(-25))/1. Factor 0*m - 2/3*m**n + 0 + 0*m**2 - 1/3*m**4.
-m**3*(m + 2)/3
Let m(x) be the second derivative of -x**6/6 - 11*x**5/4 + 5*x**4/4 + 155*x**3/6 - 55*x**2 - 152*x. Factor m(f).
-5*(f - 1)**2*(f + 2)*(f + 11)
Let i be 448/(-252) - (0 + -2). Suppose 2 - 4 = -v. Suppose i*q**v + 4/9*q + 2/9 = 0. Calculate q.
-1
Let c = -107 + 131. Let -3*z**4 - 428*z**3 + c*z + 422*z**3 - 6*z + 15*z**2 = 0. Calculate z.
-3, -1, 0, 2
Let r(z) = z**3 - 8*z**2 + z - 6. Let l be r(8). Determine b, given that -10*b**2 - 125*b + 3*b**l - 11*b**2 - 30 - 2*b**2 = 0.
-6, -1/4
Let k(v) = -159*v**2 + 156*v - 6. Let r(x) = x**3 + 317*x**2 - 311*x + 14. Let j(u) = -7*k(u) - 3*r(u). Factor j(g).
-3*g*(g - 53)*(g - 1)
Let h(n) = -n**2 - n + 1. Let z(d) = -d - 110 - 4*d - 4*d**2 + 112. Let a(x) = -6*h(x) + 2*z(x). Factor a(o).
-2*(o + 1)**2
Let b(g) be the second derivative of g**5/40 + g**4/24 - 5*g**3/6 + 2*g**2 + 486*g. Suppose b(o) = 0. What is o?
-4, 1, 2
Let z(h) be the third derivative of -h**6/32 - 27*h**5/80 + 53*h**4/32 - 21*h**3/8 + 3*h**2 + 73*h. Factor z(q).
-3*(q - 1)*(q + 7)*(5*q - 3)/4
Find n, given tha