t r be (-60)/(-70) + 592/(-756). Let n(j) be the first derivative of 5 - 1/18*j**4 - 2/9*j + 1/9*j**2 + r*j**3. Factor n(d).
-2*(d - 1)**2*(d + 1)/9
Let r(v) = v**3 + 2*v**2 + v + 5. Let t be r(0). Factor -31 + t*b**2 + 11 - 7*b**3 + 20*b + 2*b**3.
-5*(b - 2)*(b - 1)*(b + 2)
Let c = -2/33 - -8/11. Let t be (3/15)/(45/50)*9. Suppose -1/3*j**t + 0 - c*j = 0. What is j?
-2, 0
Let h(o) be the first derivative of 104*o**3/57 - 21*o**2/19 + 4*o/19 + 55. Determine c so that h(c) = 0.
2/13, 1/4
Let g(l) = -l**3 + 3*l**2 + 3*l + 4. Let s be g(4). Let m = 4691/33 + -1560/11. Suppose 0*u + m*u**2 + s = 0. What is u?
0
Suppose -8*v = -349 - 163. Factor -58*s**3 - v*s**3 - 24*s**2 + 9*s + 137*s**3.
3*s*(s - 1)*(5*s - 3)
Let o(f) be the third derivative of -f**10/40320 - f**9/20160 - f**4/12 + 3*f**2. Let w(a) be the second derivative of o(a). Factor w(r).
-3*r**4*(r + 1)/4
Let t(n) be the third derivative of n**6/6 + 7*n**5/30 - 3*n**4/4 - 2*n**3/3 - 27*n**2. Let a(m) = m**3 + m. Let g(c) = -4*a(c) - t(c). Factor g(i).
-2*(i + 1)*(3*i - 2)*(4*i + 1)
Let c(h) be the second derivative of h**5/210 - 5*h**4/42 + 25*h**3/21 + 5*h**2 + 11*h. Let l(z) be the first derivative of c(z). Factor l(s).
2*(s - 5)**2/7
Let y(d) be the first derivative of -d**4/20 - 4*d**3/5 - 18*d**2/5 - 32*d/5 + 131. Suppose y(w) = 0. What is w?
-8, -2
Let b = 54 + -24. Suppose -3*o = 3*o - b. Suppose -20/3*a + 4/3 + 4/3*a**o - 17/3*a**4 + 16/3*a**3 + 13/3*a**2 = 0. Calculate a.
-1, 1/4, 1, 2
Let p(r) be the third derivative of 3*r**4/8 - 45*r**3/2 - 23*r**2 - r. Let c be p(15). Factor 3/2*n**2 - 33/4*n**4 + c - 27/4*n**3 + 0*n.
-3*n**2*(n + 1)*(11*n - 2)/4
Let w(c) be the third derivative of 6/5*c**3 + 32*c**2 + 0*c + 1/10*c**4 + 0 + 1/300*c**5. What is p in w(p) = 0?
-6
Let v be ((-9)/15)/((-45)/25). Suppose 0*a + 10 = 5*a. Factor 0 - 1/3*l**a - v*l.
-l*(l + 1)/3
Let z(k) = 9*k**2 + 1. Let u be z(1). Let l be ((-8)/u)/((-112)/120). Factor 2*n**4 - 6/7*n**3 + 4/7*n - 6/7*n**2 + 0 - l*n**5.
-2*n*(n - 1)**3*(3*n + 2)/7
Factor 8/7*h - 10/7 + 2/7*h**2.
2*(h - 1)*(h + 5)/7
Let f(h) be the third derivative of h**6/360 + h**5/18 + 331*h**2. Factor f(v).
v**2*(v + 10)/3
What is t in -2/17*t**4 + 48/17 - 6/17*t**3 + 56/17*t + 12/17*t**2 = 0?
-2, 3
Let d(v) be the second derivative of -v**5/60 + 2*v**4/3 - 32*v**3/3 - 33*v**2/2 - 33*v. Let l(f) be the first derivative of d(f). Find p such that l(p) = 0.
8
Let v(m) = m**2 - 6*m + 11. Let g be v(4). Suppose 4 = -g*b - 0*k + 2*k, -3*k = -6. Let 1/5*y**4 - 1/5*y - 1/5*y**2 + b + 1/5*y**3 = 0. Calculate y.
-1, 0, 1
Suppose -323*p + 654*p - 331*p - 8*p**2 + 4*p**3 + 4*p**4 = 0. What is p?
-2, 0, 1
Let n(w) be the first derivative of -w**8/336 - 5*w**7/168 - w**6/8 - 7*w**5/24 - 5*w**4/12 - 2*w**3 - 9. Let c(z) be the third derivative of n(z). Factor c(r).
-5*(r + 1)**3*(r + 2)
Suppose 4*t = 3 - 19. Let m be (-16)/(-4)*2/(-36)*t. Factor m*c - 8/9 - 2/9*c**2.
-2*(c - 2)**2/9
Determine w so that 37*w**3 - 4*w**4 - 16 + 72*w + 25*w**3 - 100*w**2 - 6*w**4 - 8*w**3 = 0.
2/5, 1, 2
Let c(o) be the first derivative of 7*o**6 - 166*o**5/5 - 10*o**4 + 136*o**3/3 - 16*o**2 - 181. Find z such that c(z) = 0.
-1, 0, 2/7, 2/3, 4
Let g(h) = 60*h**4 + 205*h**3 - 925*h**2 + 970*h - 385. Let u(z) = -5*z**4 - 17*z**3 + 77*z**2 - 81*z + 32. Let v(n) = -2*g(n) - 25*u(n). Factor v(d).
5*(d - 1)**3*(d + 6)
Let n(j) be the second derivative of -18*j**7/7 + 142*j**6/5 - 56*j**5 - 200*j**4/3 + 544*j**3/3 - 96*j**2 + 2*j - 386. Solve n(t) = 0.
-1, 2/9, 2/3, 2, 6
Suppose -57 = 2*f - 69. Let c(t) be the first derivative of 0*t**2 + 3/5*t**5 + 0*t + 5 - 1/6*t**f - 3/4*t**4 + 1/3*t**3. Let c(r) = 0. Calculate r.
0, 1
Let h = -47397/5 - -9480. Factor -6/5*g + 0 - 9/5*g**2 - h*g**3.
-3*g*(g + 1)*(g + 2)/5
Let r(k) = 9*k**4 + 61*k**3 + 11*k**2 - 39*k + 7. Let x(b) = -9*b**4 - 62*b**3 - 12*b**2 + 38*b - 7. Let z(d) = -4*r(d) - 5*x(d). Factor z(q).
(q + 1)*(q + 7)*(3*q - 1)**2
Let l be (-8)/(-2) + -3 - (-4)/4. Let h(o) be the second derivative of -7/8*o**3 - 5*o + 1/4*o**4 - 3/4*o**l + 0. Let h(q) = 0. Calculate q.
-1/4, 2
Let o(b) be the third derivative of -b**8/3192 + b**7/1995 + b**6/570 - b**5/285 - b**4/228 + b**3/57 + 2*b**2 - 24*b. Let o(i) = 0. What is i?
-1, 1
Let k = -50 + 68. Let q = 91/5 - k. Factor -q*s**4 + 0*s**2 + 0*s + 0 + 1/5*s**3.
-s**3*(s - 1)/5
Find k such that -26*k**3 - 14*k**4 + 0*k**4 + 6*k**2 + 43700*k**5 + 36*k - 43702*k**5 = 0.
-3, -2, 0, 1
Suppose -38*c - 30 = -106. Factor -1/5 + 1/5*x**c - 1/5*x + 1/5*x**3.
(x - 1)*(x + 1)**2/5
Factor -2/13*s**2 + 0 - 36/13*s.
-2*s*(s + 18)/13
Let p(i) be the second derivative of i**6/15 - 9*i**5/20 + i**4 - 2*i**3/3 + 90*i. Solve p(x) = 0 for x.
0, 1/2, 2
Suppose 2*p - 4 = 3*p + 3*i, 0 = 2*p - i - 6. Determine o so that 35*o - 15*o - 41*o**2 + 5*o**p - 8*o**3 = 0.
-5, 0, 1/2
Let r(u) be the first derivative of -u**6/9 + 28*u**5/15 - 23*u**4/2 + 272*u**3/9 - 80*u**2/3 + 215. Suppose r(x) = 0. What is x?
0, 1, 4, 5
Let f(d) be the third derivative of -d**7/280 - 7*d**6/80 - 61*d**5/80 - 21*d**4/8 - 9*d**3/2 + 4*d**2 + 7*d. What is g in f(g) = 0?
-6, -1
Let h = 28 - 18. Let c = 14 - h. Factor 0*i**2 - 4*i**2 + i**4 - 4*i**5 + 2*i**c + 4*i**3 + i**4.
-4*i**2*(i - 1)**2*(i + 1)
Let v(r) be the first derivative of -3*r**6 + 168*r**5/25 - 7*r**4/5 - 32*r**3/5 + 27*r**2/5 - 8*r/5 + 60. What is z in v(z) = 0?
-4/5, 1/3, 1
Suppose 0 = 4*z, 0 = 5*j + z - 7 - 58. Let f(d) = -2*d + 26. Let x be f(j). Factor x - 1/4*i - 1/4*i**3 + 1/2*i**2.
-i*(i - 1)**2/4
Let x(l) be the third derivative of l**5/45 + 2*l**4/9 - 10*l**3/9 + 10*l**2 - l. Let x(a) = 0. Calculate a.
-5, 1
Let v(d) be the second derivative of -d**5/480 + d**4/96 - d**3/48 - 8*d**2 - 10*d. Let p(o) be the first derivative of v(o). Solve p(y) = 0 for y.
1
Let c = 4655 - 4651. Factor 0 + 0*n - 8/5*n**c - 21/5*n**3 - 18/5*n**2 - 1/5*n**5.
-n**2*(n + 2)*(n + 3)**2/5
Let m(s) = s**3 - 8*s**2 + 5*s. Let v be m(7). Let i be (v/(-12))/(10/60). Factor 3 + k**2 + 4 - i - k.
k*(k - 1)
Suppose -5*a = 2*m - 4*a, -2*m + 4*a = 0. Let x be (((-72)/15)/(-4))/2. Let -6/5*c**2 + x*c**3 + m + 3/5*c = 0. What is c?
0, 1
Let j(s) = 2 + 2 - 25*s**3 - 19*s**5 + 35*s**4 + 0 + 5*s**2. Let n(r) = r**5 - 1. Let u(h) = j(h) + 4*n(h). Factor u(g).
-5*g**2*(g - 1)**2*(3*g - 1)
Factor -7/12*h**2 + 17/12*h - 1/12*h**3 - 3/4.
-(h - 1)**2*(h + 9)/12
Let f = -65 + 65. Let w(y) be the first derivative of -13/10*y**5 + f*y + 5/12*y**6 - 1/2*y**2 + 1/6*y**3 + 1 + 9/8*y**4. Factor w(t).
t*(t - 1)**3*(5*t + 2)/2
Let h(m) = 580*m - 21324. Let s(a) = a**2 + 579*a - 21326. Let d(w) = -5*h(w) + 4*s(w). Solve d(b) = 0.
73
Let l(m) be the second derivative of 5*m**4/12 - 25*m**3/6 - 15*m**2 - 125*m. Factor l(b).
5*(b - 6)*(b + 1)
Determine p so that -8/7*p - 4/7*p**3 + 0 + 12/7*p**2 = 0.
0, 1, 2
Factor 0 + 2/9*g**3 - 10/9*g**2 + 0*g.
2*g**2*(g - 5)/9
Solve 0*d**2 + 0*d - 2/13*d**5 + 0 - 2/13*d**3 + 4/13*d**4 = 0.
0, 1
Let a be ((-1)/(-11))/(336/528). Find f, given that a*f**2 + 5/7*f**3 - 3*f - 18/7 + 1/7*f**4 = 0.
-3, -1, 2
Factor 0 + 18/7*u + 15/7*u**2 + 3/7*u**3.
3*u*(u + 2)*(u + 3)/7
Let p(s) be the third derivative of -4*s**7/1575 - 7*s**6/900 + s**5/30 + 32*s**2 - 4. Let p(k) = 0. What is k?
-3, 0, 5/4
Let n be -6 + ((-77)/(-21) - -3). Let d = -646/9 - -72. Factor -4/9 + 2/9*l**4 + n*l + d*l**2 - 2/3*l**3.
2*(l - 2)*(l - 1)**2*(l + 1)/9
Let y(o) be the second derivative of o**9/12096 - 3*o**8/4480 + 17*o**7/10080 - o**5/120 - o**4/6 + 9*o. Let j(d) be the third derivative of y(d). Factor j(k).
(k - 2)*(k - 1)**2*(5*k + 2)/4
Let y = 2 + 0. Let v(w) = w**3 + 2*w**2 - 2*w - 1. Let x be v(-2). Factor -22*z**y + 19*z**2 - 4*z**3 + z**x.
-3*z**2*(z + 1)
Suppose 48*u + 34 = 130. Let -2*v**3 - u*v**2 - 2/3*v + 0 - 2/3*v**4 = 0. Calculate v.
-1, 0
Suppose -26*l + 15 + 63 = 0. Let r(m) be the third derivative of -l*m**2 - 1/2*m**4 - 1/20*m**5 + 0*m + 0 - 3/2*m**3. Factor r(b).
-3*(b + 1)*(b + 3)
Let o(h) be the third derivative of -28*h**2 + 0*h**3 - 1/270*h**5 - 1/315*h**7 + 0*h + 1/180*h**6 + 0*h**4 + 0 + 1/1512*h**8. Factor o(p).
2*p**2*(p - 1)**3/9
Let d(k) be the first derivative of -2/3*k**4 - 1/360*k**6 - 11 + 0*k + 0*k**2 + 7/3*k**3 + 1/15*k**5. Let w(z) be the third derivative of d(z). Solve w(p) = 0.
4
Let m(x)