t u(l) be the first derivative of 6*l - 1 + 81/16*l**4 + 9/2*l**3 - 21/2*l**2 - 81/20*l**5. Factor u(n).
-3*(n + 1)*(3*n - 2)**3/4
Let k = 14 + -12. Let j(h) be the first derivative of -2/3*h**k - 2 + 2/9*h**3 + 2/3*h. Factor j(l).
2*(l - 1)**2/3
Let q = 1 + 0. Solve 2*o**2 - q - 1 + 4*o + 0*o - 4*o**2 = 0.
1
Let o(v) = -v**4 - v**2 + v. Let a(s) = s**5 - 5*s**4 - 4*s**3 - 9*s**2 + 10*s. Let u(f) = -2*a(f) + 14*o(f). Find i such that u(i) = 0.
-3, -1, 0, 1
Let m = 21 + -19. Determine r, given that -1/2*r**3 + 0 - r**m - 1/2*r = 0.
-1, 0
Let p(b) be the first derivative of 2*b + 2/5*b**5 - 4/3*b**3 - 3 + 0*b**4 + 0*b**2. Let p(v) = 0. Calculate v.
-1, 1
Let o(w) be the first derivative of -3*w**4/14 - 16*w**3/21 - 4*w**2/7 - 1. Let o(x) = 0. What is x?
-2, -2/3, 0
Let n = 229/3 + -76. Determine l so that -l**2 - l - n*l**3 - 1/3 = 0.
-1
Let p = 0 - -1. Let d = p + 1. Factor -6*v**2 - 2*v**4 + d*v**3 + 6*v**2.
-2*v**3*(v - 1)
Let u(t) be the first derivative of -t**6/20 + 4*t**5/15 - 7*t**4/12 + 2*t**3/3 + t**2 + 2. Let f(a) be the second derivative of u(a). Let f(m) = 0. What is m?
2/3, 1
Suppose 3*v + 96 = 3*s, 15 = -3*v + 3. Let j be (3/2)/(14/s). Factor 4/7*a**4 + 2/7*a + 0*a**j - 4/7*a**2 + 0 - 2/7*a**5.
-2*a*(a - 1)**3*(a + 1)/7
Let r = 359/2 + -179. Suppose -4 + 16 = -3*z, -2*z = -5*n + 8. What is i in 0 - 1/2*i**3 - r*i**5 - i**4 + n*i + 0*i**2 = 0?
-1, 0
Let r be ((-5)/2 + 2)*-4. What is x in 3*x - 2*x + 4*x**2 - 3*x**4 - 3*x**3 + x**2 - r + 2*x**3 = 0?
-1, 2/3, 1
Suppose -p - 3*x = -6, 4*p = -2*x + 1 + 3. Factor 2/5*k**3 + 0 + p*k**2 + 0*k**4 - 2/5*k**5 + 0*k.
-2*k**3*(k - 1)*(k + 1)/5
Let u = 52 + -50. Suppose 3*i - 1 = 5. Solve 4*s**i - 10*s**3 + 5*s + 2*s**u - s = 0 for s.
-2/5, 0, 1
Let p(k) be the second derivative of 3*k**5/40 - k**4/8 - k**3/4 + 3*k**2/4 + 67*k. Factor p(d).
3*(d - 1)**2*(d + 1)/2
Let z(h) = 6*h**5 + 8*h**4 + 4*h**3 + 2*h**2. Let w(b) = -25*b**5 - 33*b**4 - 17*b**3 - 9*b**2. Let g(s) = 2*w(s) + 9*z(s). Factor g(k).
2*k**3*(k + 1)*(2*k + 1)
Determine k so that 0 - 4/5*k**2 + 2/5*k**3 - 8/5*k + 1/5*k**4 = 0.
-2, 0, 2
Let f be 0*(1/2 + 0). Suppose -5*l - 25 = 0, -4*w - 3*l + 5*l + 10 = f. Factor 1/3*v + 1/3*v**2 + w.
v*(v + 1)/3
Let i(x) = x**2 + 3*x - 7. Let y be i(-5). Solve 1 - 8*z - 9 - 2*z**y - 10*z**2 - 11*z + 3*z = 0 for z.
-2, -1
Let k = -8 + 11. Find s such that 25*s + 2401*s**5 - 1400*s**2 + 230*s + 3920*s**k - 15*s - 16 - 5145*s**4 = 0.
2/7, 1
Let v(i) be the second derivative of -i**9/5040 - i**8/1120 - i**7/840 - i**4/3 - 4*i. Let p(f) be the third derivative of v(f). Factor p(r).
-3*r**2*(r + 1)**2
Let q(h) be the first derivative of 2*h**5/5 - h**4/2 - 6. Suppose q(x) = 0. What is x?
0, 1
Let q = 13 + -9. Suppose -4*h - 5*r = -15, -7 = -2*h - 4*r + r. Factor -n**h - n**q - n**5 - 3*n**4 - 2*n**3.
-2*n**3*(n + 1)**2
Let a = 55 + -52. Let s(g) be the third derivative of 1/32*g**4 + 0 + 1/12*g**a + 0*g**5 + g**2 - 1/480*g**6 + 0*g. Factor s(f).
-(f - 2)*(f + 1)**2/4
Let t be 2/(-1 - 3)*(42 + -43). Let j(x) be the first derivative of 4/3*x**3 - t*x**4 + 0*x**2 - x - 1 + 1/3*x**6 - 3/5*x**5. Suppose j(z) = 0. Calculate z.
-1, -1/2, 1
Suppose 8*l + 72 = 2*l. Let f be (-10)/6 - l/6. Let 0*y - 1/3*y**4 + f*y**3 + 0 + 0*y**2 = 0. Calculate y.
0, 1
Let s = 1 - -3. Let a(z) = 2*z**2 - 4*z - 3. Let h(q) = q**2 - 3*q - 2. Let o(l) = s*a(l) - 6*h(l). Determine c so that o(c) = 0.
-1, 0
Let 3/5*z**4 + 0*z + 21/5*z**2 + 24/5*z**3 + 0 = 0. What is z?
-7, -1, 0
Determine a, given that 0*a + 2/5*a**2 + 0 = 0.
0
Let r be (-8)/(-2 - (-2 - -2)). Let s(g) be the first derivative of 2*g + 4/3*g**3 + r*g**2 - 6/5*g**5 - 2*g**4 + 1. Determine a so that s(a) = 0.
-1, -1/3, 1
Let 16*v + 436*v**2 + 0*v**3 - 452*v**2 + 4*v**3 = 0. Calculate v.
0, 2
Let i(p) = p**3 - 9*p**2 - 10*p + 3. Let f be i(10). Suppose f*x - 6 = 6. Factor -3*n**2 + x*n**2 + 0*n + n - 2*n.
n*(n - 1)
Let q(z) be the first derivative of -3*z**4/28 - 4*z**3/7 - 15*z**2/14 - 6*z/7 + 7. Factor q(s).
-3*(s + 1)**2*(s + 2)/7
Let l be ((-2)/(-12))/((-77)/(-70)). Let y = l + 13/11. Suppose -2/3*w**2 - 2/3 + y*w = 0. What is w?
1
Let a be (-10)/(-22)*(-16)/(-10). Factor -2/11 + 4/11*f**3 - 10/11*f**2 + a*f.
2*(f - 1)**2*(2*f - 1)/11
Suppose 2*n - 17 = -t, -4*n + 11 + 29 = 4*t. Let f = n + -5. Determine u, given that -1/2*u**3 - 1/2*u**4 + 0 + 1/2*u + 1/2*u**f = 0.
-1, 0, 1
Let w be 10/4 + 1/2. Let x = w - 1. Factor 4*h**2 - 2*h**2 + 4*h**4 + 6*h**3 + 2*h**5 + x*h**4.
2*h**2*(h + 1)**3
What is x in 27*x**3 + 5*x**4 - 17*x**3 + 0*x**2 + x**2 - 10*x - 6*x**2 = 0?
-2, -1, 0, 1
Let a(g) = -g**2 - 4*g - 7. Let w(i) = -3*i - 6. Let v(j) = 3*a(j) - 4*w(j). Solve v(x) = 0.
-1, 1
Let z(l) be the third derivative of l**8/2184 + l**7/455 - l**6/195 - 5*l**2 + 1. Factor z(r).
2*r**3*(r - 1)*(r + 4)/13
Suppose 61 = 4*h + 13. Let b = -10 - -15. Factor 1 + s**4 - 1 - h*s**3 - 2*s**2 - 19*s**4 - 8*s**b.
-2*s**2*(s + 1)**2*(4*s + 1)
Let i be 184/60 + (-6)/15. Factor -2/3*a**2 - i*a - 8/3.
-2*(a + 2)**2/3
Let b = 4/15 - -1/15. Factor 1/3*h**2 + 0 + 0*h + 2/3*h**3 + b*h**4.
h**2*(h + 1)**2/3
Let z(g) be the third derivative of g**7/273 - g**6/260 - 7*g**5/390 + g**4/52 + 2*g**3/39 - 3*g**2. Solve z(p) = 0.
-1, -2/5, 1
Let w(k) be the third derivative of 0*k**5 + 0*k + 3*k**2 + 0*k**4 + 0 + 0*k**3 - 1/60*k**6. Let w(c) = 0. What is c?
0
Let n = 1082/55 + -146/11. Solve -4/5*q**4 - 4/5*q**5 + 16/5 + 4/5*q**2 - n*q + 4*q**3 = 0.
-2, 1
Let y = -631 - -634. Let 1/2*d**2 + 1/2*d**y - 2*d - 2 = 0. What is d?
-2, -1, 2
Let q(f) be the third derivative of -f**7/14 - 7*f**6/24 + f**5/2 - 8*f**2. Factor q(i).
-5*i**2*(i + 3)*(3*i - 2)
Let b(v) = -4*v**2 + 2*v - 2. Let d(l) = 9*l**2 - 3*l + 4. Let a(c) = 5*b(c) + 2*d(c). Factor a(f).
-2*(f - 1)**2
Let f(l) = 0*l**2 - 1 + 4*l**2 - l + 1. Let u be f(1). Factor 3*y**5 + 6 - y**2 - 2*y**3 + y**4 - y**u - 6.
y**2*(y - 1)*(y + 1)*(3*y + 1)
Let t(g) = -g**3 + 6*g**2 + g - 6. Let u = 23 - 17. Let q be t(u). Determine s, given that 0 - 2/9*s**3 - 2/9*s**4 + q*s + 0*s**2 = 0.
-1, 0
Let u(c) be the third derivative of -c**6/210 + c**4/14 - 4*c**3/21 - 10*c**2. Factor u(f).
-4*(f - 1)**2*(f + 2)/7
Let b = 2/85 + 73/510. Let h(j) be the second derivative of 2*j - b*j**3 - j**2 + 1/12*j**4 + 0. Factor h(z).
(z - 2)*(z + 1)
Let h be ((-20)/105)/((-2)/3). Factor 2/7*c**2 - 4/7*c + h.
2*(c - 1)**2/7
Let l(n) be the first derivative of -n + 1/8*n**4 - 11/4*n**2 + 2/5*n**5 + 2 - 2*n**3. Factor l(o).
(o - 2)*(o + 1)**2*(4*o + 1)/2
Let c = -10 - -13. Let r(s) be the second derivative of 1/6*s**4 + 1/3*s**3 + c*s + 0*s**2 + 0. Solve r(k) = 0 for k.
-1, 0
Let y(t) be the third derivative of -t**6/60 - t**5/15 + t**4/12 + 2*t**3/3 - 5*t**2. Solve y(a) = 0 for a.
-2, -1, 1
Let x(i) be the second derivative of 0 - 3/20*i**5 + 0*i**2 + 3/2*i**4 + i - 9/2*i**3. Factor x(f).
-3*f*(f - 3)**2
Let b(y) be the second derivative of 0 + 1/7*y**2 + 1/21*y**3 - 3*y - 1/42*y**4 - 1/70*y**5. Factor b(a).
-2*(a - 1)*(a + 1)**2/7
Suppose 52/3*m - 5/6*m**2 - 175/6*m**4 - 353/6*m**3 - 10/3 + 49/6*m**5 = 0. What is m?
-1, 2/7, 5
Let b be (1 + -3)/(-2 - -1). Suppose 5*q = 27 - b. Solve 0*z**2 + 2/9*z**q + 0*z + 0*z**4 + 0 - 2/9*z**3 = 0 for z.
-1, 0, 1
Factor 0 + 0*r + 8/9*r**2 + 4/9*r**4 + 4/3*r**3.
4*r**2*(r + 1)*(r + 2)/9
Let h = -1976/9 + 220. Factor 2/9 + 2/9*d**2 + h*d.
2*(d + 1)**2/9
Let z = 76/9 + -818/99. What is f in -2/11*f - 2/11*f**2 + 2/11 + z*f**3 = 0?
-1, 1
Let h(p) = 6*p**4 - 7*p**3 + 6*p**2 - 5. Let z(f) = 7*f**4 - 8*f**3 + 7*f**2 - 6. Let l(y) = 6*h(y) - 5*z(y). Find v, given that l(v) = 0.
0, 1
Factor -4*n + n**2 + 2*n + 2*n - n**3.
-n**2*(n - 1)
Factor -4*g**4 - g**3 - 6*g**4 + 9*g**4 - 2 + g + 3*g**2.
-(g - 1)**2*(g + 1)*(g + 2)
Factor -5*y**2 - 15 - 3*y**3 - 12*y**2 - 20*y - 4*y**2 - 13*y.
-3*(y + 1)**2*(y + 5)
Let c = 50/3 - 12. Suppose -3*p = -4*z + z - 12, -4*p + 10 = -z. What is x in c*x**4 + 0*x**3 - 8/3*x**2 + 0*x + p*x**5 + 0 = 0?
-2, -1, 0, 2/3
Let l(d) be the third derivative of -5*d**7/168 - d**6/16 + 11*d**5/240 + d**4/8 - d**3/6 + 8*d**2. Find j, given that l(j) = 0.
-1, 2/5
Let x(r) be the third derivative of r**6/80 - r**5/10 + 5*r**4/16 - r**3/2 + r**2. Find n such that x(n) = 0.
1, 2
Let c be ((-4)/6)/(10/30). Let b be ((-2)/4)/(3/c). Find n, given t