3*n**2. Factor x(r).
2*r*(r - 1)*(r + 1)**3/13
Let f(n) be the first derivative of 0*n**2 + 1/3*n**3 + 1/2*n**4 + 0*n + 4. Factor f(w).
w**2*(2*w + 1)
Find c such that -6/19*c**3 + 14/19*c**2 - 16/19*c**4 + 8/19*c**5 - 4/19*c + 0 = 0.
-1, 0, 1/2, 2
Let u(o) be the third derivative of 0*o**4 - 1/30*o**5 + 0*o + 0 - o**2 + 0*o**3. Factor u(l).
-2*l**2
Let l = -5 + 7. Determine r so that -5*r**2 + 0 - r**l + 2 - 4*r + 0 = 0.
-1, 1/3
Factor -4/5*p**4 - 2/5*p**5 + 0 + 0*p - 2/5*p**3 + 0*p**2.
-2*p**3*(p + 1)**2/5
Let j = 164/17 + -639/68. Factor j*w**3 + 0*w + 0 - 1/4*w**2.
w**2*(w - 1)/4
Let u(y) be the first derivative of -4*y**3/21 + 8*y**2/7 - 16*y/7 + 5. Solve u(v) = 0 for v.
2
Let j = -1 + 4. Determine x, given that 2*x**2 + 2 - x**2 - 3 - x + x**j = 0.
-1, 1
Let n(i) be the second derivative of -i**7/420 - i**6/180 + i**5/60 + i**4/12 - i**3/6 + 4*i. Let z(v) be the second derivative of n(v). Factor z(q).
-2*(q - 1)*(q + 1)**2
Let y = -10 - -14. Let a be y/(-6)*6/(-14). Let 2/7 - 2/7*z**2 - a*z**3 + 2/7*z = 0. Calculate z.
-1, 1
Factor 0*z + 0 + 2*z**2 - 1/3*z**3.
-z**2*(z - 6)/3
Factor -1/3*s + 1/3 + 1/3*s**3 - 1/3*s**2.
(s - 1)**2*(s + 1)/3
Suppose -2/3*d**5 + 4/3 + 4/3*d**3 - 8/3*d**2 + 4/3*d**4 - 2/3*d = 0. Calculate d.
-1, 1, 2
Let t(n) = 3*n - 1. Let h be t(3). Suppose 4*f + 5*j + 0 - h = 0, 4 = 2*f + 2*j. Factor -3*s**f + 5*s**2 + s + s.
2*s*(s + 1)
Let a = 127/408 - -3/136. Determine y so that 2/3*y**3 - a*y**4 - 2/3*y + 0*y**2 + 1/3 = 0.
-1, 1
Let j(q) be the third derivative of q**7/2520 - q**6/90 + 2*q**5/15 - q**4/4 + 4*q**2. Let m(t) be the second derivative of j(t). Factor m(v).
(v - 4)**2
Suppose 0*v - 5*v = -10. Solve -3*z**4 - v*z**2 + 2*z**4 + 2*z**3 + 3*z**4 + 2*z**3 - 4*z = 0 for z.
-2, -1, 0, 1
Let m(y) = 3*y**2 - 2*y - 1. Let r(x) = -x**2 + x. Let d(g) = -g**3 + 4*g**2 + 1. Let h be d(4). Let f(o) = h*m(o) + 2*r(o). Suppose f(t) = 0. Calculate t.
-1, 1
Let u(m) = -m**3 + 3*m**2 + m - 1. Let i be u(3). Let v = 302/357 + -14/51. Factor v - i*g**2 + 10/7*g.
-2*(g - 1)*(7*g + 2)/7
Solve 4*q**3 - 6*q + 4*q**2 - 2*q - 2 + 2 = 0 for q.
-2, 0, 1
Let s be 3 + -5 + (-14)/(-2). Let l(o) be the second derivative of -1/30*o**6 - 3*o + 0*o**s + 0*o**3 + 1/6*o**4 - 1/2*o**2 + 0. Let l(h) = 0. What is h?
-1, 1
Let b(p) be the second derivative of -p**4/18 + 4*p**3/3 - 12*p**2 + 4*p. Factor b(u).
-2*(u - 6)**2/3
Let f(a) be the second derivative of 4*a + 1/8*a**4 + 0 + 12*a**2 - 2*a**3. Let f(b) = 0. What is b?
4
Let h = 2574 - 28290/11. Find n, given that 16/11 + 12/11*n**2 + h*n + 2/11*n**3 = 0.
-2
Let m(q) be the first derivative of q**4/2 + 2*q**3/3 - 2*q**2 - 8. Determine s so that m(s) = 0.
-2, 0, 1
Let f(b) be the third derivative of -b**5/270 + b**3/27 + 5*b**2. Suppose f(j) = 0. Calculate j.
-1, 1
Suppose 0 = i + 2*i - 6. Let f(o) be the second derivative of 1/18*o**4 + 0 + 0*o**3 + 3*o + 0*o**i. Factor f(c).
2*c**2/3
Let j be 197/2*(9 - 11). Let x = -981/5 - j. Factor 2/5*f - x + 2/5*f**2.
2*(f - 1)*(f + 2)/5
Let r(d) be the third derivative of 0*d**3 + 0*d**4 + 4*d**2 + 0 + 1/180*d**6 + 0*d - 1/135*d**5. Let r(v) = 0. What is v?
0, 2/3
Suppose 0 + 0*v**3 + 45/7*v**5 + 132/7*v**4 + 48/7*v - 144/7*v**2 = 0. What is v?
-2, 0, 2/5, 2/3
Factor 6*b**2 - 7*b**4 + 3*b**4 + 6*b**4 + 8*b**3.
2*b**2*(b + 1)*(b + 3)
Let v(q) be the second derivative of 1/5*q**6 + 0*q**2 - 5*q + 0 + 0*q**3 + 1/6*q**4 - 3/10*q**5 - 1/21*q**7. Factor v(i).
-2*i**2*(i - 1)**3
Let u(b) be the third derivative of -6*b**7/35 - 7*b**6/30 + 11*b**5/15 + 7*b**4/6 - 4*b**3/3 + 12*b**2. Solve u(p) = 0.
-1, 2/9, 1
Let s(r) be the first derivative of r**6/2 - 6*r**5/5 - 8. Factor s(u).
3*u**4*(u - 2)
Let u = 274/5 - 54. Let m(n) be the first derivative of -3/2*n**4 - u*n + 3/5*n**2 + 28/15*n**3 - 2. What is y in m(y) = 0?
-2/5, 1/3, 1
Let s(y) = y**3 - 4*y**2 + 2*y - 6. Let g be s(4). Factor g*z**4 + z**4 - 2*z**4.
z**4
Let a = 33/38 + -6911/7980. Let r(f) be the third derivative of 1/105*f**5 + 0*f + 0 + 0*f**4 + a*f**6 + 2*f**2 + 0*f**3. Factor r(q).
2*q**2*(q + 2)/7
Let i(z) = 6*z**5 - 10*z**3 - 10*z. Let u(x) = -2*x**5 + 3*x**3 + 3*x. Suppose -3*d + 15 = 45. Let b(g) = d*u(g) - 3*i(g). Factor b(v).
2*v**5
Let x(l) = -l**2 + l - 1. Let r(u) = -3*u**3 + 19*u**2 - u - 11. Let p(i) = -r(i) - 4*x(i). Factor p(c).
3*(c - 5)*(c - 1)*(c + 1)
Let j(a) be the first derivative of -2/27*a**3 - 4/9*a - 1/3*a**2 - 1. Factor j(z).
-2*(z + 1)*(z + 2)/9
Let x be 2/6 - (-400)/24. Solve 49*z**4 + 38*z**5 - 162*z + 770*z**3 + 134*z**4 - x*z**5 - 257*z**3 + 405*z**2 = 0 for z.
-3, 0, 2/7
Let u(t) be the second derivative of 4/9*t**4 - 8*t + 1/6*t**2 + 0 - 4/9*t**3. Determine d so that u(d) = 0.
1/4
Let d = 10 + 0. Suppose -6*g = -g - d. Factor 0 - 9/2*n**g - 3/2*n + 6*n**3.
3*n*(n - 1)*(4*n + 1)/2
Let m(z) be the second derivative of -3*z**5/20 + z**3/2 + 14*z. Solve m(r) = 0 for r.
-1, 0, 1
Suppose -3*s - 1 = -7. Factor -4 - 2*o**s + 1 + 3.
-2*o**2
Let x(o) = -o + 11. Let p be x(8). Determine y, given that 0 + 2 + 2*y**4 - 2 - 2*y**p = 0.
0, 1
Let d(s) = s**3 - s**2 + s - 3. Let z be d(0). Let i = z - -5. Factor 4 - i - 2*p + 2*p**3 + 2 - 4*p.
2*(p - 1)**2*(p + 2)
Let m(n) = -42*n - 31*n**3 + 0 + 18 + 43*n**2 + 12*n**3. Let x(d) = 9*d**3 - 21*d**2 + 21*d - 9. Let z(a) = 6*m(a) + 13*x(a). Find i such that z(i) = 0.
1, 3
Let l = -552 + 554. Let 0*r + 2/9 - 2/9*r**l = 0. Calculate r.
-1, 1
Let m(u) be the second derivative of -u**5/10 - u**4/6 + u**3/3 + u**2 - 9*u. Factor m(v).
-2*(v - 1)*(v + 1)**2
Let r(o) = 5*o**2 - 5*o + 6. Suppose 3*l - 8 = 3*y + 1, -5*l - 4*y = -42. Let k(w) = -w**2 + w - 1. Let s(q) = l*k(q) + r(q). Factor s(z).
-z*(z - 1)
Let i be -7 - (-6)/36*44. Factor -2/3*b**2 + 0*b - 1/3*b**3 + 0 + i*b**4.
b**2*(b - 2)*(b + 1)/3
Let l(p) = -2*p**3 + 2*p**2 - 2. Let r(t) = -t**4 + 3*t**3 - 2*t**2 + 3. Let i(w) = 3*l(w) + 2*r(w). Factor i(s).
-2*s**2*(s - 1)*(s + 1)
Let n(k) = -6*k - 3. Let f(x) = -3*x - 1. Let a(z) = 9*f(z) - 4*n(z). Let t be a(1). Factor -1/2*m + 1/2*m**5 + t*m**3 + m**2 - m**4 + 0.
m*(m - 1)**3*(m + 1)/2
Let q = 395 - 390. Find k, given that 8/7*k**q + 0*k + 12/7*k**3 - 2/7*k**2 + 0 - 18/7*k**4 = 0.
0, 1/4, 1
Factor -10*k**5 + 4*k**2 + 16*k**5 + k**3 + k**4 - 7*k**5 - 5*k**2.
-k**2*(k - 1)**2*(k + 1)
Suppose -4*z = -3*t - z + 9, z + 27 = 5*t. Factor 7*l**2 + 3 - t*l**2 - 3.
l**2
Let i(u) be the first derivative of u**7/231 + u**6/165 - u**5/110 - u**4/66 - 3*u + 1. Let o(f) be the first derivative of i(f). Factor o(x).
2*x**2*(x - 1)*(x + 1)**2/11
Let a = 507/2 - 252. Determine j, given that 0*j**2 - a*j + 0 + 3/2*j**3 = 0.
-1, 0, 1
Let m = -56 + 56. Determine g, given that 2/7*g**4 + 0*g - 2/7*g**5 + 2/7*g**3 + m - 2/7*g**2 = 0.
-1, 0, 1
Suppose -5*a = a + a. Let t(h) be the third derivative of 1/1008*h**8 + 0 + 0*h**6 + 1/630*h**7 + 0*h**5 + 0*h - 3*h**2 + 0*h**3 + a*h**4. Factor t(y).
y**4*(y + 1)/3
Let r(m) be the third derivative of -1/45*m**5 + 1/18*m**4 + 0*m + 3*m**2 + 0 + 0*m**3 + 1/360*m**6. Let r(i) = 0. What is i?
0, 2
Let r = -1 + 3. Let t(o) = -o - 1 - 2*o**2 + r*o - o. Let v(w) = w**2 + 1. Let x(j) = -2*t(j) - 3*v(j). Determine i, given that x(i) = 0.
-1, 1
Let k(w) = 15*w**5 + 24*w**4 - 6*w**2 - 15*w. Let q(o) = o**5 + o**4 - o. Let j(c) = -k(c) + 18*q(c). Factor j(a).
3*a*(a - 1)**3*(a + 1)
Factor -d**3 + 2*d - 4*d**2 + 3*d**3 + 3 - 3.
2*d*(d - 1)**2
Let k(d) be the second derivative of -1/10*d**5 + 0*d**2 - 1/6*d**4 + 1/15*d**6 + 4*d + 0*d**3 + 0 + 1/21*d**7. Suppose k(u) = 0. What is u?
-1, 0, 1
Factor 1/2*s + 0 + 1/4*s**2 - 1/2*s**3 - 1/4*s**4.
-s*(s - 1)*(s + 1)*(s + 2)/4
Let c(u) be the first derivative of -6 + 1/5*u**3 - 6/5*u**2 + 12/5*u. Find m such that c(m) = 0.
2
Let j(g) be the first derivative of 4*g**5/5 - 4*g**4 + 16*g**3/3 + 10. Determine t so that j(t) = 0.
0, 2
Let h(w) = 18*w**5 + 34*w**4 - 50*w**3 - 34*w**2 + 2*w. Let b(i) = -i**5 - i**3 - i. Let n(v) = -10*b(v) + h(v). Suppose n(d) = 0. What is d?
-3/2, -1, 0, 2/7, 1
Let v be 3/(-3)*(-2 + -1). Suppose v*m - 5*x + 8 = 0, 0*x + 4*x = 16. Factor -g**2 + g**m + 0*g + 0*g**3 - g + g**3.
g*(g - 1)*(g + 1)**2
Factor -20/7*u + 18/7*u**2 - 6/7 + 8/7*u**3.
2*(u - 1)*(u + 3)*(4*u + 1)/7
Let t(h) be the first derivative of 12*h**5/5 - 11*h**4 + 4*h**3 + 22*h**2 - 24*h + 33. 