r) = 0.
1, 8
Let j = 14117/42369 + 2/14123. Factor -1/6 + 0*n**2 - j*n**3 + 1/3*n + 1/6*n**4.
(n - 1)**3*(n + 1)/6
Let z(r) be the third derivative of r**7/280 - r**6/16 + 29*r**5/80 - r**4 + 3*r**3/2 + r**2 + 87*r. Find w, given that z(w) = 0.
1, 2, 6
Let o = -2632/3 + 880. Let b(r) be the first derivative of o*r**3 - r**4 + 2*r**2 - 2 - 8*r. Determine j so that b(j) = 0.
-1, 1, 2
Let o = -369 - -154. Let x = 1527/7 + o. Factor 72/7*w**2 - x*w - 128/7*w**4 + 2/7 - 32/7*w**3.
-2*(w + 1)*(4*w - 1)**3/7
Let g(a) be the third derivative of a**7/1260 + a**6/675 - a**5/900 - 2*a**3 - 6*a**2. Let b(s) be the first derivative of g(s). Factor b(t).
2*t*(t + 1)*(5*t - 1)/15
Let k(c) be the third derivative of -c**8/4480 + c**7/560 - c**6/192 + c**5/160 - 3*c**3 + 5*c**2. Let p(v) be the first derivative of k(v). Factor p(z).
-3*z*(z - 2)*(z - 1)**2/8
Suppose 9*a - 150 = -132. Let r(f) be the first derivative of -1/16*f**4 - 19/6*f**3 + a*f**5 + 1 - 1/2*f + 17/8*f**2 - 2/3*f**6. Suppose r(d) = 0. Calculate d.
-1, 1/4, 1, 2
Let p be (-50)/(-5) - (-142)/(-16). Factor 9/8*t**3 + 3/8*t**5 + 0 + 0*t + 3/8*t**2 + p*t**4.
3*t**2*(t + 1)**3/8
Let j = -3795 - -3795. What is h in 2/3*h**4 + 16*h**2 + j + 32/3*h + 6*h**3 = 0?
-4, -1, 0
Let b be (20/(-25))/(1 - (-52)/(-40)). Find o such that -b*o**3 - 2/3*o**4 - 4/3*o + 0 - 10/3*o**2 = 0.
-2, -1, 0
Let j(z) be the second derivative of -3/80*z**5 + 0*z**2 - 1/48*z**4 - 8*z + 1/120*z**6 + 1/8*z**3 + 0. Find v such that j(v) = 0.
-1, 0, 1, 3
Let s = -9304 - -9307. Find z, given that -8/3*z**s + 0*z**2 + 0 + 4/3*z**5 + 4/3*z + 0*z**4 = 0.
-1, 0, 1
Let o = 81 - 195. Let w = -112 - o. Factor -w*s**3 - 3*s + 9/2*s**2 + 1/2.
-(s - 1)**2*(4*s - 1)/2
Let d(h) be the second derivative of 0*h**2 + 9/10*h**5 + 1/8*h**4 + 9/20*h**6 - 1/2*h**3 + 0 + 6*h. Suppose d(w) = 0. Calculate w.
-1, -2/3, 0, 1/3
Let f(s) = -s**2 - 1. Let x(g) be the second derivative of -23*g**4/12 + g**3/3 - 3*g**2 - 2*g + 16. Let w(c) = 30*f(c) - 5*x(c). Factor w(u).
5*u*(17*u - 2)
Let x(w) be the third derivative of -w**8/1344 - w**7/280 - w**6/480 + w**5/80 + w**4/48 + 66*w**2. What is u in x(u) = 0?
-2, -1, 0, 1
Let q(m) be the second derivative of -3/20*m**5 - m**3 + 3/14*m**7 + 0 + 0*m**2 - 1/2*m**6 + 18*m + 5/4*m**4. Let q(l) = 0. Calculate l.
-1, 0, 2/3, 1
Let k = 67 - 10. Let t = k - 113/2. Factor g**2 - 1/2*g**4 + 0 - t*g**3 + 0*g.
-g**2*(g - 1)*(g + 2)/2
Let f(m) be the second derivative of 0 + 64/9*m**3 + 2/15*m**5 - 7*m - 4/3*m**4 - 1/180*m**6 - 5/2*m**2. Let o(d) be the first derivative of f(d). Factor o(h).
-2*(h - 4)**3/3
Let n(x) = 22 + 29*x - 528*x**2 + 3*x + 548*x**2. Let c(r) = r**2 + r + 1. Let u(m) = 44*c(m) - 2*n(m). Factor u(f).
4*f*(f - 5)
Factor 55350*f**3 - 55328*f**3 - 46*f**2 - 12 + 46*f - 10*f**2.
2*(f - 1)**2*(11*f - 6)
Suppose 4*a + 32 = -4*u, 2*a = a - 3. Let f(s) = -9*s**3 + 10*s**2 + 17*s - 2. Let o(h) = -6*h**3 + 7*h**2 + 11*h - 2. Let d(r) = u*f(r) + 8*o(r). Factor d(q).
-3*(q - 2)*(q - 1)*(q + 1)
Let i(b) be the first derivative of b**4/24 + 23*b**3/18 + 43*b**2/12 + 7*b/2 + 13. Factor i(z).
(z + 1)**2*(z + 21)/6
Let c(r) be the second derivative of -r**5/12 + 5*r**4/6 + 25*r**3/6 - 23*r**2 + 27*r. Let w(d) be the first derivative of c(d). Factor w(o).
-5*(o - 5)*(o + 1)
Suppose 109 = 3*l + 4*b, -2*l - 101 = -5*l + 4*b. Let i = 38 - l. What is c in -3/4*c**2 - 3 + i*c = 0?
2
Let m(z) be the first derivative of -z**4/14 + 60*z**3/7 + 104. Factor m(a).
-2*a**2*(a - 90)/7
Suppose -3*h + 3*w = 4 - 10, w = -h. Let p(a) be the first derivative of -h - 1/26*a**4 - 12/13*a**2 + 16/13*a + 4/13*a**3. Suppose p(d) = 0. What is d?
2
Let s(h) be the third derivative of -2*h**2 - 1/5*h**5 + 0 + 0*h + 1/30*h**6 - 1/6*h**4 + 2*h**3. Factor s(w).
4*(w - 3)*(w - 1)*(w + 1)
Suppose 7 = 4*y - 9. Suppose -y*g + 0 = -8. What is t in -27*t + 142*t + 77*t - 48*t**g + 4*t**3 - 256 = 0?
4
Factor -2*s**2 - 88/9 + 80/9*s.
-2*(s - 2)*(9*s - 22)/9
Let q(x) be the first derivative of 3*x**4 - 15*x**3 + 18*x**2 + 12*x - 81. Factor q(u).
3*(u - 2)**2*(4*u + 1)
Let j(h) = 3*h**3 + h**2 - h. Let z(d) = -10*d**3 + 26*d**2 + 2*d - 30. Let s(w) = 4*j(w) + z(w). Determine q so that s(q) = 0.
-15, -1, 1
Factor -8/3*j + 3 - 1/3*j**2.
-(j - 1)*(j + 9)/3
Let p(z) = -8*z**5 - 4*z**4 + 4*z**3 + 14*z**2 - 2*z - 4. Let x(o) = o**5 - o**2. Let u(c) = -2*p(c) - 12*x(c). Suppose u(v) = 0. Calculate v.
-2, -1, 1
Let 11*f + 3*f**2 + 0*f - 2 - 10*f = 0. Calculate f.
-1, 2/3
Suppose -3*j = 3*q - 138, 0 = -5*q + 4*q + j + 38. Let w = q - 25. Solve 13*x**2 + 3*x**2 - w*x**3 + 32*x + 19*x**3 = 0.
-4, 0
Factor -2*g**2 + 547 - 264 + 100*g - 179 + 0*g**2 - 2*g**2.
-4*(g - 26)*(g + 1)
Let h = -17/182 - -631/910. Solve 1/5*k**2 - h*k + 2/5 = 0.
1, 2
Find w, given that 117 - 217 - 27*w + 10*w**2 - w**3 + 118 = 0.
1, 3, 6
Let l = 22045/115626 + -1/5506. Factor l*n + 2/21 + 2/21*n**2.
2*(n + 1)**2/21
Let b be 3 - (-4 + 148/24 - (-1)/(-2)). Factor -4/3*o**3 - 16/3 + 16/3*o**2 + b*o.
-4*(o - 4)*(o - 1)*(o + 1)/3
Factor -225/4*a + 0 + 5/4*a**2.
5*a*(a - 45)/4
Factor -1/3*v**2 - 529/3 - 46/3*v.
-(v + 23)**2/3
Let g = 36362/15 + -2424. Factor 16/15*c - 2/3*c**2 + g*c**3 - 8/15.
2*(c - 2)**2*(c - 1)/15
Let t = -2936 + 2936. Find k, given that -2/17*k**2 - 2/17*k + t = 0.
-1, 0
Let -16*q**2 + 7 - 5/2*q**3 + 23/2*q = 0. What is q?
-7, -2/5, 1
Factor -1150*a**2 - 1157*a**2 + 2311*a**2 + 8*a + 4.
4*(a + 1)**2
Let a = -5796 - -40590/7. Factor -27/7 + 3/7*x**4 - a*x + 24/7*x**2 + 18/7*x**3.
3*(x - 1)*(x + 1)*(x + 3)**2/7
Let d = -1776 - -1776. Factor d*r + 0*r**3 + 0 + 0*r**4 + 0*r**2 - 3/5*r**5.
-3*r**5/5
Suppose 0 = -9*q + 6 + 12. Suppose -16*s**2 - 12*s**q + 27*s**2 - 2*s = 0. Calculate s.
-2, 0
Let m = -417 - -421. Solve -3/7*h + 4/7*h**m - 5/7*h**2 + 1/7 + 3/7*h**3 = 0 for h.
-1, 1/4, 1
Determine u, given that 320/3*u + 820/3*u**2 - 15/2*u**5 + 0 - 115*u**4 + 290/3*u**3 = 0.
-16, -2/3, 0, 2
Let u(a) be the third derivative of a**7/420 - a**6/15 + 11*a**5/15 - 4*a**4 + 12*a**3 + 110*a**2. Solve u(l) = 0 for l.
2, 6
Let l(r) be the first derivative of -3*r**4/4 + 35*r**3 - 969*r**2/2 + 867*r + 657. Suppose l(v) = 0. Calculate v.
1, 17
Determine v, given that 24*v**2 - 46*v**2 - 3*v**3 - 129*v - 26*v**2 - 27*v - 144 = 0.
-12, -2
Let l(d) be the second derivative of -2/11*d**2 - 12*d + 1/33*d**4 - 1/110*d**5 + 0 + 1/33*d**3. Solve l(k) = 0 for k.
-1, 1, 2
Let i = -64 - -76. Let c be -3*(46/i + -4). Let -7/4*a**3 + 5/4*a**2 + 0 + c*a = 0. What is a?
-2/7, 0, 1
Let g = -14885/21 - -708. Let f = -10/21 - g. Factor -1/3 - 1/3*z + f*z**2 + 1/3*z**3.
(z - 1)*(z + 1)**2/3
Let c = 84/19 - 15616/3515. Let n = 728/555 - c. Let -2/3*m**2 + n + 2*m**3 - 2/3*m**4 - 2*m = 0. What is m?
-1, 1, 2
Suppose 0 = -2*o + 2, 2*i - 1 = -o + 4*o. Let c = -38 + 77/2. Suppose 4*q - 2 - 5/2*q**i + c*q**3 = 0. Calculate q.
1, 2
Factor 58/13*w**3 - 1080/13 + 1134/13*w - 414/13*w**2 - 2/13*w**4.
-2*(w - 20)*(w - 3)**3/13
Solve 6898*q**2 - q**4 + 8*q - 6895*q**2 - 2*q**3 + 4 + 0*q**3 = 0.
-2, -1, 2
Let g be ((-15)/(-10))/((-2)/(32/(-12))). Let v(o) be the first derivative of -1 - o + 0*o**g + 1/3*o**3. Factor v(f).
(f - 1)*(f + 1)
Let p(k) be the second derivative of k**4/42 - 2*k**3/7 - 55*k**2/7 - 4*k + 3. Suppose p(f) = 0. What is f?
-5, 11
Suppose 0 = -u - 2*h + 14, 5*h - 21 = 3*u - 2*u. Suppose 4*o + 6*o**2 - 8 - 41*o**3 + 39*o**3 - u*o = 0. Calculate o.
-1, 2
Let j = -475 - -477. Let k(b) be the first derivative of 0*b + 7 - 1/7*b**j - 2/21*b**3. Factor k(t).
-2*t*(t + 1)/7
Let l(t) be the first derivative of -6/11*t**2 + 3/11*t**4 - 20 + 6/55*t**5 - 6/11*t + 0*t**3. Solve l(f) = 0 for f.
-1, 1
Let i(j) be the first derivative of -13/3*j**3 + 9 - 36*j + 24*j**2 + 1/4*j**4. Factor i(g).
(g - 6)**2*(g - 1)
Let j(w) = 9*w**3 - 16*w**2 - 47*w + 21. Let d(c) = -3*c**3 + 5*c**2 + 16*c - 6. Let v(l) = -7*d(l) - 2*j(l). Factor v(s).
3*s*(s - 3)*(s + 2)
Let i(x) be the first derivative of x**7/1680 + x**6/60 + x**5/5 + 4*x**4/3 - 44*x**3/3 + 3. Let c(u) be the third derivative of i(u). Factor c(q).
(q + 4)**3/2
Suppose 4*h = 2*b + 38, -5*h + 15*b - 13*b = -48. Let w(l) be the second derivative of 0 - 1/3*l**4 - 4*l**3 - 5*l - h*l**2. Solve w(y) = 0 for y.
-5, -1
Let d(f) = 3*f**2 - 65*f - 45. Let a(p) = 2*p**2 - 33*p - 27.