Let b be 3/((-4)/1 + -19). Let v = 35/92 + b. Factor -1/2*p**3 + 0*p**2 + v*p**4 - 1/4 + 1/2*p.
(p - 1)**3*(p + 1)/4
Let h(b) be the first derivative of -11 + 2/9*b**3 - 2/3*b**2 + 2/3*b. Let h(u) = 0. What is u?
1
Let p(r) be the second derivative of 6*r**6/5 - 3*r**5/5 - 5*r**4/3 - 2*r**3/3 + 68*r + 1. Factor p(l).
4*l*(l - 1)*(3*l + 1)**2
Let z(f) be the third derivative of f**6/480 - f**5/5 + 8*f**4 - 512*f**3/3 - 71*f**2. Solve z(h) = 0 for h.
16
Let p(r) be the first derivative of -r**7/280 + r**6/60 - r**5/40 + 23*r**3/3 - 12. Let z(n) be the third derivative of p(n). Factor z(g).
-3*g*(g - 1)**2
Factor k**2 + 1/3*k**4 - 3*k + 5/3*k**3 + 0.
k*(k - 1)*(k + 3)**2/3
What is x in -6 - 753/2*x**2 - 147/2*x**5 + 189/2*x**4 + 543/2*x**3 + 90*x = 0?
-2, 1/7, 1, 2
Let n = -76 + 182. Let j = n - 52. Solve -21*o**3 - j + 123*o**2 + 26*o**2 - 29*o**2 - 153*o = 0.
-2/7, 3
Let t(a) be the second derivative of 3/4*a**2 + 5/8*a**3 + 1/4*a**4 + 3/80*a**5 - 3*a + 3. Factor t(s).
3*(s + 1)**2*(s + 2)/4
Let n(q) = -4*q**2 + q + 11. Let u be n(-3). Let h be (1/3)/(u/(-9) - 3). Factor 2/3*r**4 + 0*r**2 + 0*r + 0 - 2/3*r**h + 4/3*r**5.
2*r**3*(r + 1)*(2*r - 1)/3
Let s = -2275/6 + 380. Let o(h) be the first derivative of 5/4*h**4 - 25/8*h**2 - 5/2*h - s*h**3 + 5/24*h**6 + 3 + h**5. Determine i so that o(i) = 0.
-2, -1, 1
Factor -4*q**3 - 22417*q**2 - 3*q**3 + 22420*q**2 + 5*q**4 - q**5.
-q**2*(q - 3)*(q - 1)**2
Let w(a) be the second derivative of -16/15*a**3 + 0 - 1/150*a**5 - 4*a + 2/15*a**4 - 7*a**2. Let j(u) be the first derivative of w(u). Let j(i) = 0. What is i?
4
Let b(i) be the second derivative of -2*i + 1/6*i**6 + 0 + 7/80*i**5 + 11/168*i**7 + 0*i**2 - 1/24*i**4 + 0*i**3. Factor b(u).
u**2*(u + 1)**2*(11*u - 2)/4
Solve -1936 + 0*g**2 - 106*g - 4*g**2 - 103*g + 33*g = 0 for g.
-22
Let j be (-51)/(-7) - (16 + -13 + 4). Let -j*v**5 + 0*v + 0*v**2 + 4/7*v**3 + 2/7*v**4 + 0 = 0. Calculate v.
-1, 0, 2
Let b(h) be the second derivative of -9/20*h**5 + 1/10*h**6 + 0*h**2 + 3/2*h**3 + 30*h + 0 - 1/4*h**4. What is r in b(r) = 0?
-1, 0, 1, 3
Let j(r) be the first derivative of -r**3 + 3/2*r + 0*r**2 + 3/10*r**5 + 0*r**4 + 7. Factor j(f).
3*(f - 1)**2*(f + 1)**2/2
Let w = 15/7 + -17/21. Suppose 22*o + 70 - 94 = 64. Determine n, given that -4/3 - 2/3*n**3 + n**2 + w*n - 1/3*n**o = 0.
-2, 1
Let v(u) be the third derivative of -1/60*u**4 - 1/30*u**3 + 1/1050*u**7 + 0*u + 0*u**5 + 1/300*u**6 + 8*u**2 + 0. Factor v(y).
(y - 1)*(y + 1)**3/5
Suppose 0 = -v + r - 5*r + 16, -2*r = 4*v - 36. Let -1 - v + 2*y**2 + y**2 - 6*y = 0. What is y?
-1, 3
Let y(a) be the third derivative of 4/51*a**3 + 4/255*a**7 - 29/1020*a**6 + 0*a + 0 + 33*a**2 - 19/170*a**5 + 1/51*a**4. Determine z, given that y(z) = 0.
-1, -1/4, 2/7, 2
Let a(n) be the first derivative of -1/45*n**5 - 1/3*n**4 + 1/2*n**2 - 2 - 2*n**3 + 0*n. Let p(f) be the second derivative of a(f). Factor p(i).
-4*(i + 3)**2/3
Let p(d) be the second derivative of 8/7*d**3 + 14*d + 3/14*d**4 + 16/7*d**2 + 1/70*d**5 + 0. Factor p(y).
2*(y + 1)*(y + 4)**2/7
Let a(k) = -3*k**5 + 21*k**4 + 51*k**3 + 33*k**2 + 6*k. Let p(s) = s**5 - s**3 - s**2 - s. Let m(t) = -a(t) - 6*p(t). Determine j so that m(j) = 0.
-3, -1, 0
Let l(a) be the first derivative of -a**4/2 - 10*a**3/3 - 7*a**2 - 6*a + 36. Factor l(t).
-2*(t + 1)**2*(t + 3)
Let d(k) be the second derivative of 0*k**3 + 0 + 0*k**4 - 1/399*k**7 - 2/285*k**6 + 0*k**2 + 6*k - 1/190*k**5. Solve d(s) = 0 for s.
-1, 0
Factor -12*b**3 + 16*b - 2 - 70477*b**5 + b**4 + 4*b**2 + 70478*b**5 + 2.
b*(b - 2)**2*(b + 1)*(b + 4)
Let u(x) be the first derivative of 0*x - 12/5*x**2 - 23 + 8/15*x**6 + 0*x**5 + 20/3*x**3 - 27/5*x**4. Suppose u(d) = 0. Calculate d.
-3, 0, 1/2, 2
Let 5*c**4 - 34*c + 25*c**2 - 15*c - 30 + 14*c + 35*c**3 = 0. What is c?
-6, -1, 1
Let w(j) be the third derivative of -j**6/2700 + j**5/225 + j**4/36 + 5*j**3/3 + 19*j**2. Let o(l) be the first derivative of w(l). Factor o(i).
-2*(i - 5)*(i + 1)/15
Let r(s) be the third derivative of 1/18*s**4 + 1/90*s**6 + 1/18*s**3 + 1/30*s**5 + 1/630*s**7 - 13*s**2 + 0 + 0*s. Factor r(n).
(n + 1)**4/3
Let p(j) = 3*j**2 + 125*j + 126. Let o(n) = -6*n**2 - 248*n - 252. Let w(h) = -2*o(h) - 5*p(h). Factor w(k).
-3*(k + 1)*(k + 42)
Let v = -28 - -50. Factor -v*l + 8*l**2 + 2 + l**3 - l**5 - 2*l**4 + 0 + 29*l + l**3.
-(l - 2)*(l + 1)**4
Suppose -2*w + 38 - 6 = -4*g, 4*g = 4*w - 68. Let d = w + -14. Find q such that d*q**4 - 4*q**2 + 5*q**3 + 3*q**3 + 0*q**2 - 2*q**3 = 0.
-2, 0, 1/2
Let r(u) be the second derivative of -u**4/3 - 4*u**3/3 - 13*u**2/2 + 11*u. Let o(c) = -c**2 + 1. Let q(l) = 3*o(l) - r(l). Solve q(t) = 0.
-4
Let k be (-4 + 84/16)/(2/8). Let r(t) be the third derivative of 0*t - 1/156*t**4 + 6*t**2 + 0 + 1/390*t**k + 0*t**3. Find i such that r(i) = 0.
0, 1
Let p = -7 + 31. Let -3*o**2 + 4 - 6 - 14 - p*o - 5 = 0. Calculate o.
-7, -1
Let s(t) be the first derivative of -2*t + 1/4*t**4 - 1 - 1/2*t**2 + 2/3*t**3. Factor s(n).
(n - 1)*(n + 1)*(n + 2)
Suppose 5*o = -5*o + 40. Let i(y) be the third derivative of -5*y**2 + 0*y**o + 0 + 1/165*y**5 + 1/660*y**6 + 0*y + 0*y**3. Determine n so that i(n) = 0.
-2, 0
Determine t so that 12835*t**2 - 49 - 1585*t**2 + 300*t + 51 = 0.
-1/75
Suppose -8*g = -14*g + 24. Determine s so that -6*s**4 + g*s**3 - 7*s**4 + 4*s**5 + 21*s**4 = 0.
-1, 0
Suppose 0 = -2*s - 2*j + 20, -3*s + s + 2*j = -8. Suppose 2*a = u + s, -u + 5*u - 2 = 2*a. Find c, given that 0 + 2/9*c**4 + 2/9*c**2 + 0*c - 4/9*c**u = 0.
0, 1
Suppose 2*b = 2*g - 1076 + 1094, -g - 3 = 2*b. Factor 1/2 - 3/2*a - 1/2*a**3 + 3/2*a**b.
-(a - 1)**3/2
Let d(v) be the first derivative of 15/8*v**2 + 9/2*v + 1/4*v**3 + 27. Find o, given that d(o) = 0.
-3, -2
Let u(v) be the third derivative of v**5/12 + 65*v**4/4 - 400*v**3/3 - 180*v**2. Factor u(q).
5*(q - 2)*(q + 80)
Suppose -39*i + 92*i = 43*i + 30. Let 27/7 + 54/7*g - 180/7*g**2 + 134/7*g**i + 4/7*g**5 - 39/7*g**4 = 0. Calculate g.
-1/4, 1, 3
Let x be 0 - (-10)/(-15) - 1130/(-12). Let s = -92 + x. Factor -3/4*f - 3/4*f**2 + s.
-3*(f - 1)*(f + 2)/4
Let q(z) be the third derivative of -z**5/80 + 7*z**4/32 + 39*z**3/4 - 282*z**2. Let q(w) = 0. Calculate w.
-6, 13
Let q(g) be the third derivative of 1/36*g**4 + 0*g - 1/540*g**6 - 2/27*g**3 + 0 - 4*g**2 + 0*g**5. Factor q(b).
-2*(b - 1)**2*(b + 2)/9
Suppose 0 = -9*w - 728 + 2060. Let x = 152 - w. Determine r so that -4/3*r**2 + 4/3*r**3 - 2/3*r**5 - 2/3*r + 2/3 + 2/3*r**x = 0.
-1, 1
Let r(t) be the second derivative of -t**4/6 - 6*t**3 + 3*t + 43. Find m such that r(m) = 0.
-18, 0
Let 52/5*w - 16/5 + 14/5*w**2 = 0. What is w?
-4, 2/7
Suppose -3*o - 5*d - 85 - 34 = 0, -o = 4*d + 49. Let t = 33 + o. Solve 0*l**2 + 1/2*l - 3/2*l**3 - l**4 + t = 0.
-1, 0, 1/2
Find r, given that -1/3 - 1/3*r**4 - 1/6*r**5 + 2/3*r**2 + 1/3*r**3 - 1/6*r = 0.
-2, -1, 1
Suppose 5*i = 6 + 19. Factor -4*c**3 - c + 8*c**4 + 5*c**i + 2 - 10*c**2 + 4*c**2 - 4*c**2.
(c - 1)*(c + 1)**3*(5*c - 2)
Let x(c) be the second derivative of -1/42*c**7 + 0 + 3/20*c**5 + 0*c**2 + 26*c - 1/12*c**4 - 1/3*c**3 + 1/30*c**6. Let x(f) = 0. What is f?
-1, 0, 1, 2
Let y(g) = -2*g**2 - 19*g - 19. Let j be y(-8). Factor j*b**3 + 2*b**2 - 9*b - 12*b**2 - 6*b.
5*b*(b - 3)*(b + 1)
Let b(o) be the first derivative of o**6/18 - o**5/5 - o**4/4 + 7*o**3/9 + o**2 - 468. Factor b(g).
g*(g - 3)*(g - 2)*(g + 1)**2/3
Let w(k) be the third derivative of -5*k**8/336 + 4*k**7/21 + 19*k**6/12 - 130*k**5/3 + 7375*k**4/24 - 2500*k**3/3 - 255*k**2. Determine h, given that w(h) = 0.
-8, 1, 5
Let a(z) = -z**3 - 2*z + 2. Suppose 3*g + 2*g = 0. Let t be a(g). Find y such that -t - 7*y - 10*y**2 - y**2 - 2*y**3 + 4*y**2 = 0.
-2, -1, -1/2
Let i be 266/(-10) - 16/((-24)/(-6)). Let g = i + 31. Determine h, given that 0 + 2/5*h + g*h**2 = 0.
-1, 0
Let d(x) = 5*x + 11. Let m be d(5). Suppose -4*k + 120 = -m. Find c, given that 36*c + 2 - k*c + 5*c**2 - 5*c**2 + c**2 = 0.
1, 2
Let w = 39442 + -39442. Factor 2/3 + w*c - 2/3*c**2.
-2*(c - 1)*(c + 1)/3
Let l = 22 - 22. Let s(f) be the second derivative of -1/10*f**2 - 1/15*f**3 + 2*f + 0 + 1/50*f**5 + 1/150*f**6 + l*f**4. Find k such that s(k) = 0.
-1, 1
Let t(k) = -k**3 - k**2 + 2*k. Let x(h) = -6*h**3 - 4*h**2 + 11*h. Let v(m) = -33*t(m) + 6*x(m). Suppose v(j) = 0. Calculate j.
0, 