*p**2 + 4/3*p**3 + 0 + s*p - 1/12*p**4. Suppose a(b) = 0. Calculate b.
4
Let m = 5666/65 - 1050/13. Factor -m*o**2 - 84/5*o - 72/5 - 4/5*o**3.
-4*(o + 2)*(o + 3)**2/5
Let v be (-1)/(-6) + (-57)/(-36). Let k be (-6)/(-54) + 320/36. Determine a so that k*a + 15/2*a**4 - 11/2*a**2 - v*a**5 - 2 - 29/4*a**3 = 0.
-1, 2/7, 1, 2
Suppose 0 = -197*t + 199*t - 10. Factor -5*x**5 + 4*x**2 + 15*x**5 - 2*x**3 + x - 2 - 2*x**4 + 0 - 9*x**t.
(x - 2)*(x - 1)**2*(x + 1)**2
Let y(g) be the first derivative of 0*g + 4/5*g**5 + 2/3*g**6 + 4 + 0*g**4 + 0*g**2 + 0*g**3. Find o such that y(o) = 0.
-1, 0
Suppose -412*d + 10 + 3 = 13. Factor 2/7*l**5 + 0*l**4 + 4/7*l**2 - 6/7*l**3 + d + 0*l.
2*l**2*(l - 1)**2*(l + 2)/7
Let q(a) be the third derivative of -a**7/180 - a**6/24 - a**5/360 + 5*a**4/24 + 2*a**3/9 + 5*a**2 - 6*a. Suppose q(i) = 0. What is i?
-4, -1, -2/7, 1
Factor 5*r**3 - 2*r**3 - 230 + 13 - 6*r**3 - 420*r - 66*r**2 - 383.
-3*(r + 2)*(r + 10)**2
Suppose 7*l + 19 = -37. Let b be (-10)/(-5) - (-14)/l. Determine p so that 0*p + b*p**4 - 1/4*p**2 + 0*p**3 + 0 = 0.
-1, 0, 1
Let j(u) be the third derivative of 0*u + 1/180*u**5 + 1/360*u**6 + 7*u**2 - 1/18*u**3 + 0 - 1/72*u**4. Solve j(l) = 0 for l.
-1, 1
Suppose -3*y - y = -16. Let p = y - 2. Factor -2*b + 10*b**p + 2*b - 14*b**3 + 4*b.
-2*b*(b - 1)*(7*b + 2)
Suppose u - 26 = -7*v + 2*v, -4*u = -2*v - 16. Suppose u = 4*h - a, 0 = -h + 3*a - 2*a. Factor 7*q**h - 3 - q**2 + 29*q - 32*q.
3*(q - 1)*(2*q + 1)
Let s = -146 - -199. Let a = -49 + s. Determine y, given that 2/5 + 4*y**3 + 2/5*y**5 + 2*y + 2*y**a + 4*y**2 = 0.
-1
Suppose 16 = -4*w, -3*a + 4*w = 66 - 88. Factor 48/5*g + 32/5 + 18/5*g**a.
2*(3*g + 4)**2/5
Let n(h) = -4*h**3 + h**2 - 6*h. Let z(s) = 15*s**3 - 5*s**2 + 23*s. Let d(i) = 22*n(i) + 6*z(i). Factor d(m).
2*m*(m - 3)*(m - 1)
Let b(d) be the second derivative of -d**5/50 - d**4/10 + 5*d + 1. Factor b(x).
-2*x**2*(x + 3)/5
Suppose -15 = -m - 2*m - 2*c, 3*c + 5 = m. Suppose -3*h + n + 0 = -5, 0 = -3*h + m*n - 11. Let 8 + 3*l**h - 3 - 3*l - l**2 - 4 = 0. What is l?
-1, 1/3, 1
Let f = 3 - 0. Factor -9*w**4 + w**2 - 13*w**2 + 4*w**4 + 50*w**3 - 18*w**f.
-w**2*(w - 6)*(5*w - 2)
Let q be 1/((-3)/(-72)*4). Let g = q + -3. Suppose 2*c**3 - 3*c**5 + c**2 - 4*c**2 + 0*c**4 + g*c**4 + c**3 = 0. Calculate c.
-1, 0, 1
Let h(x) be the first derivative of 2*x**3/15 - x**2/5 - 12*x/5 + 56. Factor h(m).
2*(m - 3)*(m + 2)/5
Let v(u) be the third derivative of -u**8/84 + u**6/30 - 85*u**2. Factor v(n).
-4*n**3*(n - 1)*(n + 1)
Factor -25/2*s**2 - 25/6*s**3 + 14/3 - 6*s.
-(s + 2)*(5*s - 2)*(5*s + 7)/6
Factor -64 + 1/2*r**4 - 17/2*r**3 - 16*r + 39*r**2.
(r - 8)**2*(r - 2)*(r + 1)/2
Let h(f) = 48*f**2 - 23*f. Let m(c) = 120*c**2 - 57*c. Let d(s) = -12*h(s) + 5*m(s). Factor d(y).
3*y*(8*y - 3)
Let a(v) be the second derivative of -v**7/420 - v**6/240 + v**5/120 + v**4/48 + 3*v**2 - 16*v. Let j(r) be the first derivative of a(r). Factor j(k).
-k*(k - 1)*(k + 1)**2/2
Factor -2/5*k**3 - 12/5*k**2 + 14/5*k + 0.
-2*k*(k - 1)*(k + 7)/5
Let f(w) be the third derivative of -w**5/100 + 11*w**4/10 - 242*w**3/5 - 283*w**2 - 1. Determine j so that f(j) = 0.
22
Factor -2/3*i**3 + 16/3 - 4/3*i**2 + 8/3*i.
-2*(i - 2)*(i + 2)**2/3
Suppose 0 = 5*l - 5*z - 115 - 0, -l = -5*z - 27. Suppose -19 = r - l. Factor 2/5*o**4 + 0*o + 0 - 2/5*o**r + 0*o**2.
2*o**3*(o - 1)/5
Let 6/5*x - 6/5*x**3 + 0 + 6/5*x**4 - 6/5*x**2 = 0. What is x?
-1, 0, 1
Factor 39/2*v**2 - 1/2*v**3 + 20*v + 0.
-v*(v - 40)*(v + 1)/2
Suppose k + 32 = 9*k. Factor 31 - t**2 - 6 + k*t**2 + 2 + 18*t.
3*(t + 3)**2
Solve -270*k**2 - 84 - 29*k + 3*k**3 - 91*k + 237*k**2 = 0 for k.
-2, -1, 14
Let c(g) be the third derivative of -g**8/1008 + g**7/126 - g**6/40 + 7*g**5/180 - g**4/36 - 9*g**2 - 1. Find q such that c(q) = 0.
0, 1, 2
Let k(u) be the second derivative of -u**9/7560 + u**8/1680 - u**6/180 + u**5/60 - 3*u**4/2 - u. Let l(d) be the third derivative of k(d). Factor l(a).
-2*(a - 1)**3*(a + 1)
Suppose 16*z - 8 = 12*z. Factor -3*a**2 - 13*a + 5*a**3 + 3*a - z*a**2.
5*a*(a - 2)*(a + 1)
Let -12/23 + 6/23*d**3 - 8/23*d**2 - 26/23*d = 0. What is d?
-1, -2/3, 3
Find u, given that 3/4 - 3/4*u - 3/4*u**2 + 3/4*u**3 = 0.
-1, 1
Let y = 3/187 - -97/5610. Let c(j) be the third derivative of -5*j**2 + 0 + y*j**5 + 0*j**4 + 0*j + 0*j**3. Factor c(b).
2*b**2
Let s(a) be the third derivative of -a**6/480 - 17*a**5/240 - 7*a**4/48 + 4*a**3/3 + 65*a**2. What is h in s(h) = 0?
-16, -2, 1
Let u = -27914/117 - -2150/9. Suppose -4/13*s**3 + 2/13*s**2 - 2/13 + u*s = 0. What is s?
-1, 1/2, 1
Let a be (-1804)/(-2460) - (4/(-15))/(2 + -4). Let 9/5 - a*q**2 - 6/5*q = 0. What is q?
-3, 1
Suppose 6*o - 806 = -26. Let t be 145/o - (-1)/(-2). What is b in -2/13*b**2 - t + 8/13*b = 0?
2
Suppose 2518*y - 789*y - 843*y - 796*y + 5*y**2 = 0. What is y?
-18, 0
Let n(w) be the second derivative of -w**6/2520 + w**5/280 + w**3/2 + 11*w. Let d(q) be the second derivative of n(q). Factor d(h).
-h*(h - 3)/7
Factor 6*c**5 + 3*c**4 - 30*c**4 + 9*c**2 - c**2 + 73*c**2.
3*c**2*(c - 3)**2*(2*c + 3)
Factor 2/7*b**3 + 10/7*b + 12/7*b**2 + 0.
2*b*(b + 1)*(b + 5)/7
Factor -24/7 + 48/7*j + 6/7*j**5 + 6/7*j**4 - 30/7*j**3 - 6/7*j**2.
6*(j - 1)**3*(j + 2)**2/7
Factor -38*g**3 - 4*g + 224*g**2 + 12*g**4 - 14*g - 182*g**2 + 2.
2*(g - 1)**3*(6*g - 1)
Factor 800/9*r**2 + 400/9*r + 64/9 + 500/9*r**3.
4*(5*r + 2)**2*(5*r + 4)/9
Let y(p) be the first derivative of -p**3/6 + p**2/4 + p - 20. What is z in y(z) = 0?
-1, 2
Let c(o) be the second derivative of 0*o**4 + 16*o + 0*o**3 + 1/20*o**5 + 0 + 0*o**2 - 1/60*o**6. Determine v so that c(v) = 0.
0, 2
Let p(o) be the second derivative of -1/120*o**5 + 0 + 1/252*o**7 - 1/60*o**6 - 21*o + 1/24*o**4 + 0*o**2 + 0*o**3. Factor p(q).
q**2*(q - 3)*(q - 1)*(q + 1)/6
Let x be (210 - 2) + 3 + (-3 - 2). Let a = x + -206. Factor -2/7*r + a + 4/7*r**2 - 2/7*r**3.
-2*r*(r - 1)**2/7
Let z = 34 - 32. Suppose -12*r - r**2 - 20*r - 16*r - 32 - 4*r**3 - 23*r**z = 0. Calculate r.
-2
Let n = -2647 + 13243/5. Factor 0 + 0*w + 0*w**2 - 4/5*w**5 + 4/5*w**4 + n*w**3.
-4*w**3*(w - 2)*(w + 1)/5
Let -4/3*h**3 - 48 + 8/3*h**2 + 20*h = 0. What is h?
-4, 3
Factor 0*m**2 + 16/3*m**4 + 0*m - 4/3*m**5 - 16/3*m**3 + 0.
-4*m**3*(m - 2)**2/3
Let m(k) = 198*k**5 + 630*k**4 + 746*k**3 + 402*k**2 + 108*k + 2. Let c(o) = -2*o + 1. Let g(j) = 6*c(j) + m(j). Find h such that g(h) = 0.
-1, -2/3, -1/3, -2/11
Suppose 2*x = k, 6 = -2*x + 7*x - 4*k. Let w be 56/120 - x/6. Let 0 - 2/5*v**5 + 2/5*v - 4/5*v**2 + w*v**4 + 0*v**3 = 0. Calculate v.
-1, 0, 1
Let 48/7*f - 26/7*f**2 + 8/7 = 0. Calculate f.
-2/13, 2
Factor -15*p**2 - 3*p**3 + 3 + 0*p**3 - 12 + 3*p + 24.
-3*(p - 1)*(p + 1)*(p + 5)
Let 139*b**2 + 14*b - 72*b**2 - 66*b**2 = 0. Calculate b.
-14, 0
Let v(t) be the third derivative of t**5/20 - 9*t**4/4 - 2*t**2 - 80. Factor v(s).
3*s*(s - 18)
Let g(s) = -s. Let t(m) = -3*m**3 + 6*m**2 + 48*m + 72. Let y(f) = 3*f - 2. Let r be y(1). Let x(l) = r*t(l) - 12*g(l). Suppose x(u) = 0. What is u?
-2, 6
Let i be (1/84*-3)/((-4)/14). Let b(t) be the first derivative of 0*t - 3 + i*t**4 - 1/12*t**3 - 1/20*t**5 + 0*t**2. Factor b(x).
-x**2*(x - 1)**2/4
Let n(w) be the second derivative of 0 + 0*w**3 + 2/63*w**4 + 1/63*w**6 - 8*w - 8/105*w**5 + 25/441*w**7 + 0*w**2. Factor n(y).
2*y**2*(y + 1)*(5*y - 2)**2/21
Let m be (-2 + 13)*(-92)/(-506). Let 2/7 + 2*p + 18/7*p**m - 20/7*p**4 - 2*p**3 = 0. Calculate p.
-1, -1/2, -1/5, 1
Suppose 0 = 4*r + p - 13, -242*r - 5*p = -247*r + 10. Find j such that 1/3*j**4 - j**2 + 0 + 0*j + 2/3*j**r = 0.
-3, 0, 1
Let j(d) be the first derivative of -d**3/9 - 3*d**2/2 + 52*d/3 - 83. Solve j(l) = 0 for l.
-13, 4
Let k(z) = 0 - 2 + 2*z - 4*z**2 + 3*z**2. Let w(r) = -5*r**2 + 8*r - 9. Let f be 8/5 + 2/5. Let m(u) = f*w(u) - 9*k(u). Suppose m(x) = 0. Calculate x.
-2, 0
Let t(z) be the second derivative of z**7/14 - z**6/2 + 9*z**5/20 + 5*z**4/4 - 2*z**3 - z + 31. Solve t(h) = 0 for h.
-1, 0, 1, 4
Let g(r) = 19*r**2 - 65*r + 12. Let l(u) = 40*u**2 - 131*u + 24. Let f(d) = 5*g(d) - 2*l(d). Let f(c) = 0. What is c?
1/5, 4
Let x be (26/(-2457)*-36)/((-15)/(-35)). Suppose -x*t**2 + 2/9*t**4 + 4/9*t + 2/3 - 4/9*t**3 = 0. Calculate t.
-1, 1, 3
Let b(u) be the second derivative of u**7/105 - 7*u**6/75 - u**5/5 + 8*u**4/15 + 29*u 