**4 - g**3 + g + 1. Let x(p) = 12*p**4 + 10*p**3 + 8*p**2 - 10*p - 20. Let b(h) = 28*u(h) + 2*x(h). Determine m so that b(m) = 0.
-3, -1, 1
Let n = -1374 + 10993/8. Let k(p) be the first derivative of -1/2*p**3 - 1/2*p - n*p**4 - 2 - 3/4*p**2. Factor k(r).
-(r + 1)**3/2
Let g(x) be the second derivative of -3/8*x**5 + 0*x**2 - 1/4*x**4 - 1/28*x**7 + 0 + 0*x**3 - 1/5*x**6 + 3*x. Factor g(n).
-3*n**2*(n + 1)**2*(n + 2)/2
Let i(f) be the third derivative of f**9/113400 + 3*f**4/8 + 14*f**2. Let r(d) be the second derivative of i(d). Factor r(c).
2*c**4/15
Let q(x) be the third derivative of x**6/280 - 9*x**5/140 + 3*x**4/7 - 10*x**3/7 + x**2 + 17*x. Factor q(f).
3*(f - 5)*(f - 2)**2/7
Suppose 5*f - 10 = 20. Determine x so that 48*x**3 + 5*x - 26*x**4 + 3*x + f*x**4 - 36*x**2 = 0.
0, 2/5, 1
Suppose 3*n + 12 = 3*s, -s - 5*n = -5*s + 17. Let -10*w**2 + 9*w**5 + 2*w - 5*w**2 - 8*w - 3*w**s + 15*w**4 = 0. What is w?
-1, -2/3, 0, 1
Let z(k) be the first derivative of 2*k**5/35 + 3*k**4/14 - 4*k**2/7 + 20. Factor z(b).
2*b*(b - 1)*(b + 2)**2/7
Let z = -3 + 5. Suppose 6*r - 10*r - 16 = -4*b, -4*r = -3*b + 14. Determine q so that 3 + q**z - 3*q + 3 - 10*q**b = 0.
-1, 2/3
Let t(o) be the first derivative of 1/50*o**5 + 0*o + 4/15*o**3 - 1/8*o**4 + 2 - 1/5*o**2. What is f in t(f) = 0?
0, 1, 2
Let a(n) be the first derivative of 25/12*n**3 + 6 + 5/2*n**2 + n. Factor a(u).
(5*u + 2)**2/4
Let z(l) = 2*l**3 - 12*l**2 - 21*l + 51. Let h be z(7). Factor -10/7 + 8/7*v + 2/7*v**h.
2*(v - 1)*(v + 5)/7
What is x in 8*x**2 - 38*x + 80824 + 3*x**3 - 80806 - 19*x = 0?
-6, 1/3, 3
Determine m so that 480*m + 250 + 4/5*m**3 - 198/5*m**2 = 0.
-1/2, 25
Let r(q) = 4*q**2 + 6*q + 5. Let v(x) = 7*x**2 + 11*x + 9. Suppose 10 + 5 = 3*t. Let c(n) = t*r(n) - 3*v(n). Factor c(j).
-(j + 1)*(j + 2)
Suppose -3*a + 195 - 183 = 0. Let w(g) be the second derivative of 5*g + 0*g**2 + 1/26*g**a + 2/39*g**3 - 1/195*g**6 + 0*g**5 + 0. Factor w(z).
-2*z*(z - 2)*(z + 1)**2/13
Let l = 17 - -14. Find s such that 44*s**2 + 1 + s**4 + 3 - 12*s - l*s**2 - 6*s**3 = 0.
1, 2
Factor 0 + 3/4*g**2 + 1/8*g**3 + 0*g.
g**2*(g + 6)/8
Suppose 0 = -8*l + 12*l - 8. Let 91*i**3 + 2*i**4 - 5*i**4 - 82*i**3 - 6*i**l = 0. Calculate i.
0, 1, 2
Let a(u) be the first derivative of u**5/50 + u**4/10 - u**3/15 - 3*u**2/5 + 5*u - 12. Let j(t) be the first derivative of a(t). Factor j(k).
2*(k - 1)*(k + 1)*(k + 3)/5
Let a(j) be the third derivative of 2*j**2 + 0 + 1/72*j**4 - 2/315*j**7 + 1/45*j**5 + 0*j - 1/360*j**6 + 0*j**3. Factor a(l).
-l*(l - 1)*(l + 1)*(4*l + 1)/3
Let s(l) be the first derivative of l**4/16 - 3*l**3/4 + 3*l**2 - 4*l + 54. Factor s(y).
(y - 4)**2*(y - 1)/4
Let c(b) = -24*b**2 - 12*b - 34. Let s(p) = 2*p**2 + 2*p + 2. Let g(h) = -2*c(h) - 22*s(h). Factor g(n).
4*(n - 3)*(n - 2)
Let p(l) = -10*l**2 - 7*l**2 + 2*l + 19*l**2 - 5*l**2. Let s(m) = -16*m**2 + 11*m. Let c(u) = 11*p(u) - 2*s(u). Factor c(i).
-i**2
Let v be (-6)/(-24) - 11/(-4). Determine p, given that -4*p + 6*p**v - 3*p**2 + 11*p**2 + 4*p**3 - 14*p**3 = 0.
0, 1
Suppose 15*i - 13*i = 4*x - 14, -4*x + 18 = 2*i. Let p(d) be the second derivative of 0 + 1/6*d**x + 2*d**2 - 6*d - d**3. Find l, given that p(l) = 0.
1, 2
Let s(y) be the first derivative of 8*y**3/27 - 13*y**2/9 + 2*y/3 - 590. Factor s(w).
2*(w - 3)*(4*w - 1)/9
Let -12*k**3 + 121/2 - 132*k + 83*k**2 + 1/2*k**4 = 0. What is k?
1, 11
Let t(q) be the first derivative of 27*q**4/8 - 3*q**3/2 - 15*q**2/4 - 3*q/2 + 72. Factor t(u).
3*(u - 1)*(3*u + 1)**2/2
Let o(p) = -p**3 + p + 1. Let a(f) = f + 7. Let z be a(-11). Let n(c) = -4*c - 4. Let s(x) = z*o(x) - n(x). Solve s(q) = 0 for q.
0
Let w(c) be the second derivative of -3*c**5/10 + 5*c**4/3 + 3*c**3 + 4*c**2 + 7*c. Let d(g) = -g**3 + g**2. Let z(p) = -8*d(p) + w(p). Factor z(u).
2*(u + 1)**2*(u + 4)
Factor 0 + 0*b - 4/3*b**5 + 16/3*b**2 + 20/3*b**4 - 32/3*b**3.
-4*b**2*(b - 2)**2*(b - 1)/3
Let w(s) = -s**2 + 12*s - 18. Let n be w(10). Let 7 + 1 - 5*c + 2*c**n - 3*c = 0. What is c?
2
Let w be 21*5/20*(-150)/(-175). Solve 3/2*c**2 + 3 + w*c = 0 for c.
-2, -1
Suppose 10*s**2 + 13*s - 8*s - 5*s**2 = 0. What is s?
-1, 0
Factor -32*u**3 - 24*u**4 - 4*u**2 + 4*u**4 + 8*u + 90 - 90.
-4*u*(u + 1)**2*(5*u - 2)
Let s(r) be the second derivative of 8*r + 3/4*r**5 + 0*r**2 + 0 + 5/6*r**3 - 1/6*r**6 - 5/4*r**4. Factor s(o).
-5*o*(o - 1)**3
Suppose 3 - 25 = -2*a - 4*o, 0 = -2*a - 5*o + 25. Suppose m - 4 = -m - 4*i, 18 = a*m + 2*i. Factor 2*h**2 - 3*h - 1 - m*h + 8*h.
(h + 1)*(2*h - 1)
Let h = -733 - -3677/5. Find n such that -h*n - 4/5*n**2 + 0 = 0.
-3, 0
Let a(u) be the second derivative of 3*u + 0*u**4 + 1/3*u**3 + 0 + 1/240*u**6 - 1/40*u**5 - 5/2*u**2. Let i(b) be the first derivative of a(b). Factor i(t).
(t - 2)**2*(t + 1)/2
Let 0 - 24/5*a + 14/5*a**2 - 2/5*a**3 = 0. Calculate a.
0, 3, 4
Suppose -2397*x - 66 = -2430*x. Factor 9/4 + 1/4*a**4 + a**3 - 1/2*a**x - 3*a.
(a - 1)**2*(a + 3)**2/4
Suppose -25 = -3*b + 5*d, 4*d = 3*b + 6 - 26. Suppose 2*r + 3*r = -4*h + 16, 4*r = 0. Let b*w**2 - 4 - w + 2*w**2 - h*w**2 - 5*w = 0. Calculate w.
-2, -1
Let r(z) = -2*z**2 - 37*z - 46. Let s be r(-17). Let l(g) be the second derivative of 4*g + 0*g**4 + 3/140*g**s + 0*g**2 + 0 - 1/14*g**3. Solve l(w) = 0 for w.
-1, 0, 1
Let k(g) be the first derivative of -3 + 1/7*g**2 + 0*g - 2/21*g**3. Find d, given that k(d) = 0.
0, 1
Factor 79707*n**2 - 326*n**3 - 8661494*n + 1/2*n**4 + 705911761/2.
(n - 163)**4/2
Let n be 11 + (-57)/(-24) - 13. Factor -3/2*q - n*q**2 + 3/8*q**3 + 3/2.
3*(q - 2)*(q - 1)*(q + 2)/8
Solve -9*q + 4*q**2 - 7*q**2 + 5*q**2 + 13*q = 0 for q.
-2, 0
Let x(p) = 8*p**4 - 104*p**3 - 186*p**2 - 25*p + 49. Let z(f) = f**4 + f**3 - f**2 + 1. Let h(j) = x(j) - 3*z(j). Factor h(b).
(b - 23)*(b + 1)**2*(5*b - 2)
Suppose 78*v - 83*v = -15. Let m(d) be the first derivative of 6/5*d + 4 - 4/5*d**2 + 2/15*d**v. Factor m(k).
2*(k - 3)*(k - 1)/5
Let y(c) be the second derivative of c**5/70 + c**4/14 + 28*c. Factor y(w).
2*w**2*(w + 3)/7
Factor 147*s**5 + 50*s**3 + 655*s**3 - 268*s**4 + 120*s - 257*s**4 - 221*s**2 - 12 - 214*s**2.
3*(s - 1)**3*(7*s - 2)**2
Let a(o) be the second derivative of -o**6/30 + 23*o**5/10 - 44*o**4 - 23*o**3/3 + 529*o**2/2 + 109*o. Suppose a(x) = 0. What is x?
-1, 1, 23
Let j(y) be the third derivative of -y**7/1050 + 29*y**6/300 + 6*y**2 + 2. Find a, given that j(a) = 0.
0, 58
Let a(n) = -16*n**4 - 163*n**3 - n**2 + 115*n - 44. Let t(q) = -8*q**4 - 82*q**3 + 58*q - 22. Let b(m) = -6*a(m) + 13*t(m). What is k in b(k) = 0?
-11, -1, 1/2
Suppose 21*q - 20*q = 16. Let k be (54/72)/(42/q). Let -6/7*p - k*p**3 + 2/7 + 6/7*p**2 = 0. Calculate p.
1
Suppose 3*r = 25*r. Let f(k) be the second derivative of 0*k**3 + 0*k**2 + 0*k**4 + r + 3*k + 1/150*k**5 - 1/225*k**6. Factor f(n).
-2*n**3*(n - 1)/15
Suppose 2*b = 2*b - b. Let r be ((0 + b)/(-1))/(-17 - -18). Factor r*k - 1/3*k**5 + 0 + 1/3*k**4 + 1/3*k**3 - 1/3*k**2.
-k**2*(k - 1)**2*(k + 1)/3
Let o = 49/16 - 19/16. Factor -o*g + 3/4 - 21/8*g**2.
-3*(g + 1)*(7*g - 2)/8
Let l(u) = -5*u**2 + 11*u - 8. Let c(b) be the first derivative of -4*b**3/3 + 5*b**2 - 8*b - 35. Let i(k) = -3*c(k) + 2*l(k). Find j such that i(j) = 0.
2
Let s(i) be the second derivative of -i**5/20 + 11*i**4/12 - 16*i**3/3 + 14*i**2 - 97*i + 1. Determine k so that s(k) = 0.
2, 7
Let v = -4 - -6. Suppose -3*z = v*s - 8*z - 4, s - 5*z = 2. Factor -7*g**s + 9*g**2 - g**3 + 3*g**3.
2*g**2*(g + 1)
Let x be 493/51 + -10 - (-32)/6. Let z(b) be the first derivative of 4/5*b**x + b**4 + 0*b - 4/3*b**3 - 7 - 2*b**2. Factor z(r).
4*r*(r - 1)*(r + 1)**2
Let m = -143 - -79. Let x = 67 + m. Factor 1/3*k**x + 0 + 0*k - 1/6*k**4 - 1/6*k**2.
-k**2*(k - 1)**2/6
Solve 9*r**4 + 18*r - r**4 + 6*r - 28*r**2 - 4*r**4 = 0.
-3, 0, 1, 2
Let s be 667/5 - (-24)/6. Let z = s - 137. Factor -2/5*h**2 + 4/5 - z*h.
-2*(h - 1)*(h + 2)/5
Let x(n) be the first derivative of -n**6/6 - n**5/2 + 5*n**4/12 + 5*n**3/3 - 9*n + 14. Let b(j) be the first derivative of x(j). Factor b(o).
-5*o*(o - 1)*(o + 1)*(o + 2)
Determine t so that -12*t**4 - 2*t**3 - 21*t - 6*t**3 + 29*t + 12*t**2 = 0.
-1, -2/3, 0, 1
Suppose 5*k = -44 - 6. Let z = k - -12. Factor 7*n**2 + 2*n**3 - 7*n**2 - z*n**2 + n**4 - n - n**5 + 1.
-(n - 1)**3*(n + 1)**2
Let c = 14815 - 44444/3. Factor -c*a**3 +