-90) + 22/9. Let y be 10 + -2 - 3 - 1. Factor 0*i**3 + 0 + y*i**2 - f*i - 4/3*i**4.
-4*i*(i - 1)**2*(i + 2)/3
Let t(g) be the second derivative of g**7/42 - g**6/5 + 9*g**5/20 + g**4/3 - 2*g**3 - 1017*g. Factor t(q).
q*(q - 3)*(q - 2)**2*(q + 1)
Suppose 9 = -18*j + 21*j. Factor 49*y**2 + 9*y**4 + 38*y - j*y + 18*y - 57*y**3 + 10.
(y - 5)*(y - 2)*(3*y + 1)**2
Let b = 13 - 11. Let p(o) = -o**2 + 9*o + 12. Let j be p(10). Factor g**2 - 8*g**4 - b + 13*g**4 + 2 - j*g**5 - 4*g**3.
-g**2*(g - 1)**2*(2*g - 1)
Let d(g) = 3*g - 61. Let r be d(21). Factor 11*p**2 + 5*p**2 - 19*p**r - 9*p - 6.
-3*(p + 1)*(p + 2)
Let i be (-2040)/(-1530) + 8/(-18). Factor 0 - i*f**3 - 4/9*f - 2*f**2.
-2*f*(f + 2)*(4*f + 1)/9
Let c(r) be the third derivative of -r**8/588 + 4*r**7/735 + r**2 - 65. Factor c(t).
-4*t**4*(t - 2)/7
Let c(d) = 8 + d - 2 + 4. Let m be c(-8). Factor 12 + 14*g**m - 30*g + 8 - 2 - 2*g**3 + 0*g**3.
-2*(g - 3)**2*(g - 1)
Let s = 9918/5 + -1962. Factor -4/5*l**3 - 972/5*l - 2916/5 - s*l**2.
-4*(l + 9)**3/5
Factor -3*d**4 + 7*d**3 + 3*d**2 - 8*d**3 - 6*d + 7*d**3.
-3*d*(d - 2)*(d - 1)*(d + 1)
Let d(a) be the third derivative of a**8/840 + a**7/105 + 7*a**6/300 - a**5/150 - 2*a**4/15 - 4*a**3/15 - 159*a**2. Determine p, given that d(p) = 0.
-2, -1, 1
Let d(q) = -11*q**3 - 27*q**2 + 78*q - 118. Let j(u) = -9*u**3 - 25*u**2 + 77*u - 117. Let k(t) = 5*d(t) - 6*j(t). Factor k(x).
-(x - 7)*(x - 4)**2
Let g = -1287 + 1292. Let y(x) be the second derivative of -2/3*x**3 - 1/10*x**g + 0 + 1/2*x**4 - 5*x + 0*x**2. Factor y(u).
-2*u*(u - 2)*(u - 1)
Suppose 61 = 2*q - 3*k, -2*q + k + 14 = -53. Factor q*z - 36*z**2 - 6*z + 36*z**4 - 8*z**3 - 21*z.
4*z*(z - 1)*(z + 1)*(9*z - 2)
Let u(m) = -2*m**3 - 3*m**2 + 15*m + 16. Let y be u(-1). Factor -1/2 - 1/2*s**4 + 0*s**3 + y*s + s**2.
-(s - 1)**2*(s + 1)**2/2
Let h be 6/27*36/32. Factor h*b**2 + 1 - b.
(b - 2)**2/4
Suppose -7 = -4*d - 15. Let p = d + 7. Let 3*h**3 - 6*h + p*h + 2*h**2 + 4*h**2 + 4*h = 0. Calculate h.
-1, 0
Factor 16/3 - 4*s**4 - 8*s + 2/3*s**5 + 22/3*s**3 - 4/3*s**2.
2*(s - 2)**3*(s - 1)*(s + 1)/3
Let w be (-29)/4 + 5/20. Let n be 4/(-42)*(w + 12 + -11). Factor 0 + 0*v - n*v**2.
-4*v**2/7
Let f = -502 - -507. Let u(r) be the third derivative of 1/240*r**f - 1/24*r**3 + 0 + 0*r - 1/480*r**6 + 1/96*r**4 + r**2. Factor u(x).
-(x - 1)**2*(x + 1)/4
Let q(g) be the second derivative of -g**6/1080 - g**5/90 - g**4/18 + 4*g**3/3 - 10*g. Let c(u) be the second derivative of q(u). Factor c(b).
-(b + 2)**2/3
Let d(c) be the second derivative of 1/4*c**3 + 3/2*c**2 - 4*c - 3/40*c**5 - 1/4*c**4 + 0. Factor d(a).
-3*(a - 1)*(a + 1)*(a + 2)/2
Let o be (-1)/(-2) - 22/(-4). Suppose -5*l + o = -2*l. Solve -9*u**3 - 3*u**l + 4*u**5 - 4*u**2 - 2*u**5 - 5*u**4 - 2*u - 3*u**5 = 0 for u.
-2, -1, 0
Let y(w) = -14*w**3 - 14*w**2 + 2*w + 13. Let k(h) = -h**3 - h**2 + 1. Let z(d) = 26*k(d) - 2*y(d). Factor z(c).
2*c*(c - 1)*(c + 2)
Let r(j) be the first derivative of -j**4/24 + 3*j + 5. Let k(b) be the first derivative of r(b). Find f, given that k(f) = 0.
0
Solve -2/3*f**4 + 0 - 14/3*f**2 + f**5 - 16/3*f**3 - f = 0 for f.
-1, -1/3, 0, 3
Let o = 6 - -19. Let z be (-1)/(-5) + (-70)/o*-1. Let -14/3*t - 2/3*t**z - 10/3*t**2 - 2 = 0. What is t?
-3, -1
Factor 4/7*z**2 - 4/7 - 10/7*z**3 + 10/7*z.
-2*(z - 1)*(z + 1)*(5*z - 2)/7
Let l(z) be the first derivative of -z**3/7 + 519*z**2/7 - 89787*z/7 - 914. Let l(p) = 0. Calculate p.
173
Factor 3 + 3/5*y**2 + 18/5*y.
3*(y + 1)*(y + 5)/5
Let x be 1*(-2 + 106/(-6)). Let m = -19 - x. Factor -4/3*g - m*g**4 + 0*g**2 + 4/3*g**3 + 2/3.
-2*(g - 1)**3*(g + 1)/3
Suppose 50*m = 57*m + 49. Let w be 116/18 + m + 1. Factor -w*g - 2/3*g**2 - 2/9*g**3 + 0.
-2*g*(g + 1)*(g + 2)/9
Let d(x) be the second derivative of -x**6/40 + x**5/6 - x**4/6 - 4*x**3/3 + 13*x**2/2 - 17*x. Let j(o) be the first derivative of d(o). Solve j(w) = 0.
-2/3, 2
Suppose 7*z = -62 - 120. Let h be ((-4)/33)/(z/117). Factor h*r + 4/11 + 2/11*r**2.
2*(r + 1)*(r + 2)/11
Let o(g) be the first derivative of -g**6/60 - g**5/20 + g**3/6 + g**2/4 + 16*g - 5. Let y(x) be the first derivative of o(x). Suppose y(t) = 0. What is t?
-1, 1
Let t(s) be the second derivative of 363*s**5/140 - 66*s**4/7 + 45*s**3/14 - 3*s**2/7 - 132*s - 3. Factor t(i).
3*(i - 2)*(11*i - 1)**2/7
Let b(c) be the first derivative of 0*c**2 - 8*c + 2/3*c**3 - 24. Suppose b(s) = 0. Calculate s.
-2, 2
Let z = 416 + -4159/10. Let r(s) be the second derivative of 9*s - z*s**4 + 8/15*s**3 + 1/75*s**6 - 1/25*s**5 - 4/5*s**2 + 0. Factor r(g).
2*(g - 2)*(g - 1)**2*(g + 2)/5
Factor 9*f**2 + 20*f**2 - 33*f - 104 - 24 + 4*f**3 - 39*f + 31*f**2.
4*(f - 2)*(f + 1)*(f + 16)
Let n(w) be the first derivative of -w**4/30 - 2*w**3/15 - 2*w**2/15 + 70. Factor n(v).
-2*v*(v + 1)*(v + 2)/15
Let f(q) be the first derivative of 3*q**6/2 + 498*q**5/25 + 801*q**4/10 + 388*q**3/5 - 27*q**2/2 - 30*q + 189. Let f(x) = 0. What is x?
-5, -1, -2/5, 1/3
Factor 5*a**2 - 15*a**4 + 58*a - 15*a**3 + 4*a**4 - 7*a**2 - 43*a**3 + 13*a**4.
2*a*(a - 29)*(a - 1)*(a + 1)
Let f = -105 - -108. Let 2*g**3 + 3*g**2 + 3*g**5 - 7*g**3 + 2*g**3 - f*g**4 = 0. Calculate g.
-1, 0, 1
Let r(n) be the first derivative of -2*n**3/3 - 8*n**2 - 32*n - 202. Solve r(v) = 0 for v.
-4
Suppose -10*o - 32 = -42. Let n be o/(14/(-4) - -4). Determine y so that 1/2*y**3 - n*y**2 + 1/2*y**4 + 0 - 2*y = 0.
-2, -1, 0, 2
Let n(f) be the third derivative of -f**5/20 + 9*f**4/8 + 5*f**3 + 191*f**2. Suppose n(j) = 0. What is j?
-1, 10
Let c(g) be the third derivative of -2/15*g**5 + 11*g**2 - 8/105*g**7 + 1/6*g**6 + 0 + 0*g + 1/84*g**8 + 0*g**3 + 0*g**4. Factor c(o).
4*o**2*(o - 2)*(o - 1)**2
Determine x so that -1304*x**2 - 15*x + 16*x**4 + 1460*x**2 + 26*x**3 - 33*x - 122*x**3 - x**4 = 0.
0, 2/5, 2, 4
Factor 0*o + 8*o**2 + 0 - 1/2*o**3.
-o**2*(o - 16)/2
What is o in 46*o - 12 - 46*o + 9*o**2 - 6*o**2 = 0?
-2, 2
Find k, given that 11*k + 17*k + 2*k**2 + 805 - 837 + 2*k**2 = 0.
-8, 1
Let i(q) be the third derivative of -q**5/35 - 101*q**4/56 - 25*q**3/14 + q**2. Factor i(p).
-3*(p + 25)*(4*p + 1)/7
Let g(a) = a**2 + 18*a + 20. Let i be g(-17). Suppose -3*t**i - 9*t**4 - 7*t**5 + 9*t**2 - 8*t**5 + 6*t + 12*t**5 + 0*t**4 = 0. What is t?
-2, -1, 0, 1
Let x be ((-2340)/(-260) - (0 + 0)) + (0 - 6). Solve -49/3*i**x + 0 - 28/3*i**2 - 4/3*i = 0 for i.
-2/7, 0
Let f(b) be the second derivative of 15/2*b**2 - 2 + 5/3*b**3 - 5/12*b**4 - 24*b. Factor f(p).
-5*(p - 3)*(p + 1)
Suppose q = -2*y + 157, -4*y - 4 - 183 = -q. Let h = 171 - q. Factor -2/5*r**h + 0*r**3 + 0 + 2/5*r**2 + 0*r.
-2*r**2*(r - 1)*(r + 1)/5
Let c(k) = -5*k**2 - 225*k - 1210. Let i(m) be the third derivative of m**5/20 + 14*m**4/3 + 605*m**3/6 - 30*m**2. Let b(y) = 2*c(y) + 5*i(y). Factor b(q).
5*(q + 11)**2
Let o(x) be the second derivative of -5*x + 0*x**5 + 0*x**3 - x**2 - 1/15*x**6 + 1/3*x**4 + 0. Suppose o(q) = 0. What is q?
-1, 1
Let d be (7 - (-9 - -20))*7/(-14). Factor 0 - 1/8*o**d + 1/4*o**3 + 0*o.
o**2*(2*o - 1)/8
Suppose -p - 2 = -5. Factor -3*y + 4 + p + 4*y**2 - 5*y - 3.
4*(y - 1)**2
Let b = 2839/5103 - 4/5103. Factor -2/9 - 4/9*g**2 + 1/9*g**3 + b*g.
(g - 2)*(g - 1)**2/9
Suppose -24 = 6*x - 36. Let q(h) be the third derivative of 0*h**5 - 1/6*h**4 - 1/84*h**8 + 0*h**3 + 0*h**7 + 0*h + 1/15*h**6 + 0 + x*h**2. Solve q(p) = 0.
-1, 0, 1
Suppose 3*x + 3*x - 18 = 0. Factor -13*k**2 + 4*k**2 - 11*k + 2*k + x*k**4 + 3*k.
3*k*(k - 2)*(k + 1)**2
Let 7/5*y**4 - 12/5*y + y**2 + 24/5*y**3 + 0 = 0. Calculate y.
-3, -1, 0, 4/7
Let a = 791 - 786. Let f(r) be the second derivative of 0 + 5*r - 1/20*r**a + 1/6*r**4 + 2/3*r**3 - 4*r**2. Factor f(d).
-(d - 2)**2*(d + 2)
Suppose d + 3*d = 5*f - 2, 0 = -4*f + 5*d - 2. Let 3*u**5 + u**2 + 8*u**2 - 3*u**f + 15*u**3 + 12*u**4 = 0. Calculate u.
-2, -1, 0
Let a be (14 - 1)/(23 - 24). Let z be a/6 + 2 + (-26)/(-12). Factor 10/9*y**z + 0 - 4/9*y.
2*y*(5*y - 2)/9
Let f = 52 - 1559/30. Let u = f - -1/10. Factor 0 + 0*y + 2/15*y**3 - u*y**4 + 4/15*y**2.
-2*y**2*(y - 2)*(y + 1)/15
Determine l, given that -30/7 + 4/7*l**2 - 11/7*l + 1/7*l**3 = 0.
-5, -2, 3
Factor 3899 + 35*a + 5*a**3 + 50*a**2 - 7947 + 3958.
5*(a - 1)*(a + 2)*(a + 9)
Let d(n) be the third derivative of n**5/12 - 5*n**4/2 - 70*n**3/3 + 92*n**2. What is s in d(s) = 0?
-2, 14
Suppose -3*m = 2