2*(p - 1)*(p + 2)
Let j(v) be the first derivative of v**4/2 + 10*v**3/3 + 6*v**2 + 35. Determine x, given that j(x) = 0.
-3, -2, 0
Determine k so that 3/7*k**3 + 9/7*k**4 + 0 + 0*k**2 + 6/7*k**5 + 0*k = 0.
-1, -1/2, 0
Let n = 211 + -1475/7. Find q, given that n + 2/7*q**2 + 4/7*q = 0.
-1
Let s(c) be the third derivative of 1/20*c**5 + 1/12*c**3 + 0 + 0*c + 10*c**2 - 7/48*c**4. Factor s(d).
(d - 1)*(6*d - 1)/2
Solve -9/4 + 1/4*r**4 + 3/2*r**3 + 2*r**2 - 3/2*r = 0 for r.
-3, -1, 1
Let i(n) be the third derivative of 1/36*n**4 + 0 + 2*n**2 - 1/18*n**3 + 0*n - 1/180*n**5. Factor i(w).
-(w - 1)**2/3
Let s(v) = 3*v**2 - 4*v - 7. Let q(m) be the third derivative of m**5/60 - m**4/12 - m**3/2 + 5*m**2. Let o(r) = -15*q(r) + 6*s(r). Factor o(d).
3*(d + 1)**2
Suppose f - 7 + 3 = 0. Let y(r) be the second derivative of -1/6*r**f - r**2 - 2/3*r**3 + 0 - 2*r. Determine b so that y(b) = 0.
-1
Let s(l) be the third derivative of -11*l**7/630 + l**6/36 + l**5/15 - 5*l**4/36 - l**3/18 + 14*l**2. Find i, given that s(i) = 0.
-1, -1/11, 1
Suppose 189 = -3*t - 213. Let w = -398/3 - t. Factor 2/3*j**2 + 0 + w*j**3 - 2/3*j.
2*j*(j + 1)*(2*j - 1)/3
Let b = 182/3 + -157/3. Let -1/3 - 10/3*w - b*w**2 = 0. What is w?
-1/5
Suppose 3*v = 8*j - 9*j + 3, 2*j + 5*v = 6. Let h(y) be the first derivative of -4 - 12*y**4 + 0*y + 7/2*y**6 - 4*y**j + 0*y**2 - 3*y**5. What is f in h(f) = 0?
-1, -2/7, 0, 2
Suppose -5*i + 15 = 3*n, n = -7*i + 3*i + 12. Factor -1 + c**3 + 0*c**3 + c**2 - c + n*c.
(c - 1)*(c + 1)**2
Find a such that -28/9*a - 16/9 - 8/9*a**2 + 4/9*a**3 = 0.
-1, 4
Let n = -360 + 3968/11. Factor 8/11 + 2/11*q**2 + n*q.
2*(q + 2)**2/11
Let u(o) = 9*o**3 - 8*o**2 + o + 13. Let w(s) = 4*s**3 - 4*s**2 + 6. Suppose -2 + 0 = z. Let d(l) = z*u(l) + 5*w(l). Solve d(m) = 0 for m.
-1, 1, 2
Let u = 4/3 - 14/15. Find f, given that -4*f**2 - 2/5 - 2*f - 2*f**4 - 4*f**3 - u*f**5 = 0.
-1
Let x(f) = -2 - 25*f + 1 + 0 - 23*f**2 + 6*f. Let u(p) = 11*p**2 + 10*p + 1. Let t(c) = -5*u(c) - 2*x(c). Solve t(a) = 0.
-1, -1/3
Solve 2/3*l**2 + 2*l + 4/3 = 0 for l.
-2, -1
Let h(b) be the third derivative of b**4/24 - b**3/3 + b**2. Let u be h(5). Solve 2*r**2 - 4*r**u + 2*r - 2*r + 2*r**4 = 0 for r.
0, 1
Let w(h) be the third derivative of -h**7/210 + h**6/60 + 3*h**2. Determine k, given that w(k) = 0.
0, 2
Solve -56*c - 7*c**2 - 3*c**4 + 38*c + 15*c**4 - 5*c**2 + 2*c**5 + 16*c**3 = 0 for c.
-3, -1, 0, 1
Let b = -4/415 + 1054112/1245. Let n = b - 834. Factor 2/3*z + 4/3 - 14/3*z**4 + n*z**3 - 10*z**2.
-2*(z - 1)**3*(7*z + 2)/3
Let i be (-824)/56 + 4/(-14). Let l = 107/7 + i. Factor 2/7*b + l*b**5 - 4/7*b**3 + 0*b**2 + 0*b**4 + 0.
2*b*(b - 1)**2*(b + 1)**2/7
Let f be ((-4)/2)/((-5)/10). Suppose 3*z - z = f. Let 8/5 + 98/5*d**4 - 8*d - 6/5*d**z + 28*d**3 = 0. What is d?
-1, 2/7
Let 24 + 4*o**2 - 4*o - 7*o**2 - o**2 = 0. What is o?
-3, 2
Let s be (2 + -1 - 11)/(-2). Let d(c) be the third derivative of 0 + 1/360*c**6 + 0*c**3 - 1/180*c**s + 0*c**4 + 2*c**2 + 0*c. Let d(h) = 0. What is h?
0, 1
Let l be ((-94)/8)/(2/(-10)). Let x = 59 - l. Find u, given that -3/4*u - x - 1/4*u**3 - 3/4*u**2 = 0.
-1
Let z(b) = -b**4 - b**3 - b**2 + b. Let g(f) = 6*f**4 - 3*f**3 + 26*f**2 - 23*f. Let x(h) = -4*g(h) - 20*z(h). Find m, given that x(m) = 0.
0, 2, 3
Let n(q) be the second derivative of q**7/189 - q**6/45 + q**5/30 - q**4/54 - 10*q. Factor n(u).
2*u**2*(u - 1)**3/9
Let i = 5 + 0. Let m(q) be the second derivative of -1/42*q**4 + q - 1/35*q**6 - 3/70*q**i + 0 + 0*q**3 + 0*q**2 - 1/147*q**7. Let m(s) = 0. What is s?
-1, 0
Let c = -309 + 1551/5. Factor 0 + 2/5*b - c*b**2.
-2*b*(3*b - 1)/5
Factor 3/2*n + 1/2*n**2 + 0.
n*(n + 3)/2
Find v, given that 4/3*v + 1/3 + v**2 = 0.
-1, -1/3
Suppose -3*h - 19 = -28. Let v(t) = t**3 + 6*t**2 - t - 2. Let o be v(-6). Find m, given that -12/7*m**h - 8/7*m**o + 0 - 8/7*m**2 - 2/7*m**5 - 2/7*m = 0.
-1, 0
Let s be 3/(-2) + 3/2. Let w(k) be the third derivative of -1/6*k**4 + 1/30*k**5 + k**2 + 0*k + 1/3*k**3 + s. Solve w(y) = 0 for y.
1
Let k(h) be the second derivative of h**7/42 - h**6/10 - 9*h**5/20 + 23*h**4/12 + 4*h**3 - 18*h**2 - 30*h. Find p, given that k(p) = 0.
-2, 1, 3
Let u(w) be the second derivative of w**7/21 + 2*w**6/15 - w**5/5 - 2*w**4/3 + w**3/3 + 2*w**2 + w. Suppose u(o) = 0. Calculate o.
-2, -1, 1
Let n(s) be the third derivative of s**6/180 + s**5/60 - s**4/6 + 5*s**3/6 - 4*s**2. Let p(u) be the first derivative of n(u). Let p(z) = 0. What is z?
-2, 1
Let a(o) = 4 - o + o**2 + 3*o - o. Let v(y) be the first derivative of -y**2 - 3*y + 1. Let i(z) = -5*a(z) - 6*v(z). Factor i(r).
-(r - 1)*(5*r - 2)
Let y(c) be the second derivative of c**10/75600 - c**8/5600 + c**7/3150 + 5*c**4/12 - c. Let r(s) be the third derivative of y(s). Factor r(j).
2*j**2*(j - 1)**2*(j + 2)/5
Solve 2 - 33 + 26*k**2 - k**2 + 190*k - 49 = 0.
-8, 2/5
Let i(l) be the third derivative of 1/6*l**4 + 0*l + 0 + 0*l**3 + 1/24*l**6 - 1/210*l**7 - 2/15*l**5 + 6*l**2. Factor i(c).
-c*(c - 2)**2*(c - 1)
Let l be 153/45 + 2/(-5). Let b(m) be the second derivative of -m + 5/2*m**4 - 7/3*m**l + m**2 - 13/10*m**5 + 0 + 4/15*m**6. Find n, given that b(n) = 0.
1/4, 1
Let q(l) be the first derivative of l**6/21 + 2*l**5/35 - l**4/7 - 4*l**3/21 + l**2/7 + 2*l/7 - 24. Factor q(v).
2*(v - 1)**2*(v + 1)**3/7
Let y(p) be the first derivative of -p**3/27 - 30. Factor y(g).
-g**2/9
Let d(v) be the second derivative of 0*v**2 + 2*v + 1/8*v**4 + 0 - 3/40*v**5 + 1/60*v**6 - 1/12*v**3. Factor d(x).
x*(x - 1)**3/2
Let d(u) be the third derivative of 2*u**7/105 - 7*u**6/120 + u**5/30 + u**4/24 - 42*u**2. Factor d(c).
c*(c - 1)**2*(4*c + 1)
Let d(w) be the second derivative of -1/8*w**5 + 0 - 7/12*w**3 + 1/2*w**2 + 3/8*w**4 - 3*w + 1/60*w**6. Factor d(x).
(x - 2)*(x - 1)**3/2
Suppose 3*z = 4*d + 23, 3*z - 8 = 2*d + 5. Let h(k) = -6*k**3 - 2*k**2 - 6*k. Let f(l) = -l**3 - l. Let o(c) = z*h(c) - 5*f(c). Factor o(t).
-t*(t + 1)**2
Let v = 107 - 102. Let i(p) be the second derivative of -3/8*p**4 - 1/2*p**3 + 2*p - 1/4*p**2 + 0 - 1/10*p**v. What is f in i(f) = 0?
-1, -1/4
Let z(y) be the second derivative of y**6/30 - y**5/10 - 51*y. Factor z(n).
n**3*(n - 2)
Suppose -30*n = -35*n + 15. Let y(w) be the third derivative of -1/30*w**5 + 0*w - 1/30*w**4 + 0*w**n - 1/75*w**6 + 0 + w**2 - 1/525*w**7. Factor y(x).
-2*x*(x + 1)**2*(x + 2)/5
Let l(u) be the third derivative of -u**6/300 - u**5/30 - 7*u**4/60 - u**3/5 + u**2. Factor l(z).
-2*(z + 1)**2*(z + 3)/5
Let p(h) be the first derivative of -1/6*h**3 + 3 - 9/2*h - 3/2*h**2. Determine s, given that p(s) = 0.
-3
Determine g, given that -50/11 - 2/11*g**2 - 20/11*g = 0.
-5
Let l(c) be the second derivative of 3*c**5/140 + 15*c**4/28 + 9*c**3/2 + 21*c**2/2 + 24*c + 2. Factor l(s).
3*(s + 1)*(s + 7)**2/7
Let v be 0 + 30/44 + (-1)/2. Let n(i) be the first derivative of 2/33*i**3 + 2 + 0*i - v*i**2. Factor n(z).
2*z*(z - 2)/11
Let t(n) be the second derivative of n**5/120 + n**4/72 - 9*n. Solve t(j) = 0 for j.
-1, 0
Let n(g) be the third derivative of -g**8/21 + 2*g**7/35 + g**6/30 - 7*g**2. Factor n(l).
-4*l**3*(l - 1)*(4*l + 1)
Let 7/2*q**5 + 8*q**4 + 0 + q**2 + 11/2*q**3 + 0*q = 0. What is q?
-1, -2/7, 0
Let c(v) = -v + 18. Let r be c(15). Factor 9*n**r - 3*n**2 - 13*n**2 - 4*n**4 + 7*n**3.
-4*n**2*(n - 2)**2
Let k be -2 + 0 + 2 + 4. Suppose -2*w**3 + 4*w**4 - 4*w + k*w = 0. What is w?
0, 1/2
Suppose 49 = 5*q - 3*b, -42 = -5*q - b - 5. Suppose i = -i + q. Factor 4/5*w**5 + 0 + 2/5*w**3 + 0*w + 0*w**2 + 6/5*w**i.
2*w**3*(w + 1)*(2*w + 1)/5
Let k(z) be the third derivative of -z**6/360 + z**5/180 - 7*z**2. Let k(f) = 0. What is f?
0, 1
Factor 2/7*h + 2/7*h**2 + 0.
2*h*(h + 1)/7
Let w(b) be the first derivative of b**5/60 + b**4/12 + b**3/6 + b**2/2 + 1. Let u(k) be the second derivative of w(k). Determine l so that u(l) = 0.
-1
Let w(g) be the first derivative of 2/9*g**3 + 5 + 0*g - 2/3*g**2. Factor w(d).
2*d*(d - 2)/3
Suppose 2*b = -5*b - 63. Let d(g) = g**4 + 6*g**3 - 4*g**2 + 2*g - 2. Let f(c) = -5*c**4 - 25*c**3 + 16*c**2 - 9*c + 9. Let u(q) = b*d(q) - 2*f(q). Factor u(m).
m**2*(m - 2)**2
Let o = 28/13 - 71/39. Find c such that -2/3 + o*c**2 + 1/3*c = 0.
-2, 1
Suppose -8*j + 5*j = -12. Factor 0*q**2 + 4*q**2 - 3*q**2 + j*q.
q*(q + 4)
Let q(n) be the first derivative o