1/3*j**4 - 1/3*j**3 + 0*j.
j**2*(j - 1)*(j + 1)**2/3
Suppose 4*p - 2*u - 8 = 0, 5*p - u = 5 + 8. Determine a so that 6*a**p + 68 - 68 - 9*a**2 - a**4 = 0.
0, 3
Let l(q) be the second derivative of 7*q**4/36 - 59*q**3/18 + 4*q**2 - 692*q. Solve l(j) = 0.
3/7, 8
Let z be (-2 - (-60)/33) + (-338)/(-44). Let s = -6 + 8. Find k such that -45/4 + z*k - 5/4*k**s = 0.
3
Let g(q) be the first derivative of 2*q**2 - 12*q - 5. Let c be g(5). Determine f, given that c*f + f**2 + 10*f - 20*f = 0.
0, 2
Determine z, given that 6*z**5 + 8*z + 0 - 14*z**3 + 104/3*z**4 - 104/3*z**2 = 0.
-6, -1, 0, 2/9, 1
Let i be 2 - 1*(-67 - 2). Let p = i + -35. Factor 2*t**2 - t**4 + 6*t**2 - 3*t**4 - 16*t**3 - p + 48*t.
-4*(t - 1)**2*(t + 3)**2
Let h = 101 + -97. Let r(d) be the third derivative of 0*d**3 - 1/8*d**h - d**2 - 1/60*d**5 + 1/60*d**6 + 0*d + 0. Factor r(p).
p*(p + 1)*(2*p - 3)
Let k(s) be the first derivative of -s**5/180 + 5*s**4/36 - 25*s**3/18 + 33*s**2/2 + 21. Let i(g) be the second derivative of k(g). Factor i(d).
-(d - 5)**2/3
Let k(a) = -2*a**4 - 288*a**3 - 15912*a**2 - 264970*a + 281238. Let t(y) = -y**3 - y - 1. Let h(l) = 2*k(l) + 44*t(l). Factor h(w).
-4*(w - 1)*(w + 52)**3
Let o = -10 - -17. Suppose 2*m - 11 + o = 0. Factor 2*v + 12*v**m + 3*v + 4*v - 3.
3*(v + 1)*(4*v - 1)
Suppose -4*f = -8*f + 8. Factor -r**2 - r**2 + r**2 - 8*r - 3*r**f.
-4*r*(r + 2)
Let o(r) be the second derivative of -r**6/24 + r**5/3 - 5*r**4/8 - r**2 - 6*r. Let b(x) be the first derivative of o(x). Factor b(u).
-5*u*(u - 3)*(u - 1)
Let z = 34586/19 - 1820. Factor 0*d**2 - z*d - 4/19 + 2/19*d**3.
2*(d - 2)*(d + 1)**2/19
Factor -15*z + 57 + 79 + 4*z**2 - 125*z.
4*(z - 34)*(z - 1)
Let c(m) = -m**2 - 7*m + 9. Let i be c(-8). Let y = i - -1. Determine f so that -3 - 4*f**3 + 6 + f**3 - 4*f - 5*f + 9*f**y = 0.
1
Let w(s) be the third derivative of s**6/180 + s**5/20 + 7*s**3/3 - 2*s**2. Let p(y) be the first derivative of w(y). Find f such that p(f) = 0.
-3, 0
Let i(d) be the second derivative of -d**7/189 + d**6/27 - d**5/90 - 7*d**4/18 + 2*d**3/3 + 143*d. Let i(c) = 0. Calculate c.
-2, 0, 1, 3
Let q(d) be the first derivative of d**6/3 - 14*d**5/5 + 11*d**4/2 - 10*d**3/3 - 46. Factor q(l).
2*l**2*(l - 5)*(l - 1)**2
Let c be ((-4)/4 - -1)/(-3) - -3. Suppose 37*d**2 - 11*d**2 - 12 - 9*d**2 - 8*d**2 + 3*d**c = 0. What is d?
-2, 1
Factor 31*q + 5 + 4*q**2 - 30*q - 20*q**2 + 11*q**2 - q**3.
-(q - 1)*(q + 1)*(q + 5)
Let t = 5489 - 5489. Solve -4/7*q**3 + 4/7*q**2 + 0*q + t = 0 for q.
0, 1
Let g(d) = -2*d**3 - 62*d**2 - 168*d - 100. Let a(u) = -u**3 - u**2 + 2*u - 2. Let j(c) = 2*a(c) + g(c). Factor j(z).
-4*(z + 1)*(z + 2)*(z + 13)
Suppose -12 = -g - 5*g. Let k(w) be the first derivative of -g + 0*w**2 + 1/15*w**6 + 0*w**5 + 0*w - 1/10*w**4 + 0*w**3. Factor k(z).
2*z**3*(z - 1)*(z + 1)/5
Let i(s) be the first derivative of s**4/12 + 2*s**3/9 - 5*s**2/6 - 2*s + 49. Solve i(g) = 0 for g.
-3, -1, 2
Let j(f) be the first derivative of 2*f**3/3 + 73*f**2 + 98. Factor j(t).
2*t*(t + 73)
Let o(y) be the first derivative of -1/3*y**3 + 1/12*y**6 + 0*y + 17 + 1/5*y**5 - 1/4*y**2 + 0*y**4. Factor o(c).
c*(c - 1)*(c + 1)**3/2
Let l = 10025/6 - 5011/3. Factor -1/6*u**3 + 1/6*u - l*u**2 + 1/3*u**4 + 1/6.
(u - 1)**2*(u + 1)*(2*u + 1)/6
Let d = 87 + -85. Find c such that -8*c**3 - 7*c**2 - 32 + 16*c + 4*c**d + 19*c**2 + 4*c**5 - 2*c**4 - 3*c**5 = 0.
-2, 2
Let p = 193803329/693 - 279658. Let t = p + -3/77. Factor 14/9*n**3 + 0*n + t*n**2 + 0.
2*n**2*(7*n + 2)/9
Let l(n) be the third derivative of 0 + 10*n**2 + 0*n + 1/8*n**4 + 0*n**3 - 1/20*n**5. Suppose l(u) = 0. What is u?
0, 1
Let y(m) be the first derivative of 4*m**3/21 + 31*m**2/14 - 8*m/7 - 369. Determine p so that y(p) = 0.
-8, 1/4
Factor -2/9*g**3 - 14/9*g**2 - 10/3*g - 2.
-2*(g + 1)*(g + 3)**2/9
Factor 0 + 8/5*b**2 + 0*b + 4/5*b**4 - 12/5*b**3.
4*b**2*(b - 2)*(b - 1)/5
Let m(u) be the second derivative of -5*u - 5/48*u**4 - 1/3*u**3 - 1/2*u**2 + 0 - 1/80*u**5. Determine t, given that m(t) = 0.
-2, -1
Let q(x) = -11*x**3 - 26*x**2 - 68*x - 29. Let g(w) = -2*w**3 - w**2 + 1. Let t(c) = -21*g(c) + 3*q(c). Find u, given that t(u) = 0.
-2, -2/3, 9
Let o(k) = k**2 - 7*k - 2. Let x be o(8). Suppose x = c + c. Factor -3*p**c - 2*p**2 + p**5 - 140 + 140.
p**2*(p - 2)*(p + 1)**2
Factor -80 - 347*w**3 - 465*w + 1243*w**2 - 364*w**2 + 27*w**4 - 70 + 56*w**3.
3*(w - 5)**2*(w - 1)*(9*w + 2)
Let t(x) be the second derivative of 2*x**6/105 + 3*x**5/7 + 16*x**4/7 - 128*x**3/21 + 123*x. Determine n, given that t(n) = 0.
-8, 0, 1
Suppose 0 = 9*k + 18, k + 6 = 2*n - 2*k. Solve 1/2*u**4 - 7/6*u**2 + 1/6*u**5 + 2/3 + n*u - 1/6*u**3 = 0.
-2, -1, 1
Solve 24 + 27/2*n**2 - 36*n - 3/2*n**3 = 0.
1, 4
Factor -3/5*d**2 + 0*d + 12/5.
-3*(d - 2)*(d + 2)/5
Suppose 51*v - 24 = 47*v. Suppose 0 = 4*n - n - 6. Find x, given that -n*x**2 + v*x - 7*x - x = 0.
-1, 0
Let n be -34 + 42 + -27 + 22. Factor -4/5*x**n - 28*x + 44/5*x**2 + 20.
-4*(x - 5)**2*(x - 1)/5
Let g(h) be the third derivative of h**8/168 - h**6/15 + h**5/15 + h**4/4 - 2*h**3/3 - 171*h**2. Let g(d) = 0. Calculate d.
-2, -1, 1
Let p = 8 - -1. Suppose -p*x = -5*x - 8. Factor -23 + 4*v**2 - 32*v - 41 - 7*v**2 - v**x.
-4*(v + 4)**2
Suppose 0 = 5*a - 9 - 16. Factor -10*r + 0*r**3 + 0*r**4 + 0*r**4 + 10*r**3 + 5 - a*r**4.
-5*(r - 1)**3*(r + 1)
Let w(x) be the second derivative of -49*x**6/1080 + 7*x**5/90 - x**4/18 - 4*x**3/3 - 5*x. Let o(c) be the second derivative of w(c). Factor o(h).
-(7*h - 2)**2/3
Let r(n) be the second derivative of n**4/6 + 2*n**3 - 375*n. Factor r(a).
2*a*(a + 6)
Let f(t) = -3*t - 2 + 8*t - 3*t + 2*t**2. Let d be f(-2). Factor 0*b - 2/7*b**d + 0.
-2*b**2/7
Let c(u) be the second derivative of -1/2*u**5 + 0*u**2 + 0*u**3 + 0*u**4 - 1/6*u**6 - 17*u + 0. Factor c(v).
-5*v**3*(v + 2)
Let x = 169/129 - -1/43. Let c be (-24)/(-76) + (-8201)/(-15846). Suppose 5/3*d**2 - 1/3 - x*d**4 - 2/3*d**3 + c*d**5 - 1/6*d = 0. Calculate d.
-1, -2/5, 1
Let s(g) be the first derivative of 2*g**3/27 - 61*g**2/9 + 692. Solve s(q) = 0.
0, 61
Let d(x) = x**2 + 25*x + 66. Let h be d(-24). Solve -1156*l**2 + 76 - h + 408*l - 70 = 0 for l.
3/17
Factor -8*w - 17*w**2 - 9 + 16*w**2 + 9.
-w*(w + 8)
Factor -1/5*p**3 - 153/5*p - 324/5 - 22/5*p**2.
-(p + 4)*(p + 9)**2/5
Suppose 4/3*b + 2/3*b**2 + 2/3 = 0. Calculate b.
-1
Find n such that -7213*n + 10290 - 33*n**3 + 4058*n - 3*n**4 + 6536*n + 189*n**2 = 0.
-7, 10
Let m(d) be the third derivative of -2/315*d**5 + 0*d**3 + 0*d - 13*d**2 + 0 + 1/63*d**4 - 1/36*d**6. Factor m(g).
-2*g*(5*g + 2)*(7*g - 2)/21
Let 3/8*m**4 - 285/8*m**2 - 18*m - 69/4*m**3 + 0 = 0. Calculate m.
-1, 0, 48
Let n(u) be the first derivative of -2*u**3/9 - 74*u**2 - 8214*u + 514. Suppose n(o) = 0. Calculate o.
-111
Let p(u) be the second derivative of u**7/420 + u**6/80 + u**5/60 + 39*u**2/2 + 2*u. Let m(a) be the first derivative of p(a). Suppose m(j) = 0. What is j?
-2, -1, 0
Let z(i) be the first derivative of -13 + 5*i**2 + 2/3*i**3 + 12*i. Determine b so that z(b) = 0.
-3, -2
Factor 12/5*c**3 - 3/5*c**4 + 0*c + 0 - 12/5*c**2.
-3*c**2*(c - 2)**2/5
Factor -2/5*k**3 + 0 - 722/5*k + 76/5*k**2.
-2*k*(k - 19)**2/5
Let h(k) be the first derivative of 11*k**4/14 + 326*k**3/21 + 256*k**2/7 - 104*k/7 - 388. Solve h(z) = 0 for z.
-13, -2, 2/11
Let r(p) be the first derivative of -12 - 4/3*p**3 + 8*p + 2*p**2. Let r(x) = 0. What is x?
-1, 2
Let q = -57 + 84. Let b = q - 19. Factor p**3 - 4*p**4 - 20*p**2 - b*p + 0*p**3 - 2*p**3 - 15*p**3.
-4*p*(p + 1)**2*(p + 2)
Factor -12/5*k**3 + 0*k + 0 + 2/5*k**4 - 14/5*k**2.
2*k**2*(k - 7)*(k + 1)/5
Let w(h) be the third derivative of -h**7/42 - h**6/4 - 5*h**5/12 - 133*h**2. Let w(v) = 0. Calculate v.
-5, -1, 0
Let u = 3676/11 - 25710/77. Solve 0 - u*r**3 + 2/7*r - 3/7*r**2 = 0.
-2, 0, 1/2
Let i(v) be the third derivative of 0*v + 1/4*v**4 + 5*v**2 - 1/30*v**5 + 0*v**3 + 0. Factor i(n).
-2*n*(n - 3)
Factor 0 + 6*u**3 + 0*u**2 + 2/5*u**4 + 0*u.
2*u**3*(u + 15)/5
Let m(x) be the second derivative of -x**7/5880 - x**6/1260 - 5*x**3/6 - 23*x. Let v(y) be the second derivative of m(y). Determine o so that v(o) = 0.
-2, 0
Factor -240 + 2363*z + 274*z**2 - 2358*z - 5*z**3 - 34*z**2 + 2*z**3 - 2*z**3.
-5*(z - 48)*(z - 1)*(z + 1)
Let f(s) be the third derivative of -1/150*s**5 - 22