*t**3 + 4*t**2 + 8*t. Let z(i) = -3*d(i) + 8*m(i). Solve z(y) = 0.
-1, 0, 2
Let i be 1/3*(21 + -20). Solve -2/3 - v + 0*v**2 + i*v**3 = 0.
-1, 2
Determine f so that -f**4 + 511*f**3 - 2*f**2 - 513*f**3 + f**2 = 0.
-1, 0
Let b = -4 - -4. Suppose 3*r + b = 12. Suppose 20*g**2 + 14*g**5 + 5*g**4 + 24*g**3 + 4*g + 30*g**3 + 41*g**r + 6*g**2 = 0. Calculate g.
-1, -2/7, 0
Let p(j) be the first derivative of j**4 - 4*j**3/3 - 10. Factor p(v).
4*v**2*(v - 1)
Let f(l) be the second derivative of -l**7/840 + l**6/240 + l**5/20 - l**4/12 - 5*l. Let s(d) be the third derivative of f(d). Factor s(p).
-3*(p - 2)*(p + 1)
Let l(p) be the first derivative of -2/5*p + 1/10*p**2 + 1/15*p**3 - 3. Factor l(n).
(n - 1)*(n + 2)/5
Suppose -4*j - 2*y + 8 = -6, -13 = -3*j - y. Let n(r) be the second derivative of -5/16*r**4 - r - 1/2*r**2 + 0 + 2/3*r**3 - 1/40*r**5 + 1/24*r**j. Factor n(z).
(z - 1)**2*(z + 2)*(5*z - 2)/4
Let a be ((-1)/(-3))/(7/105). Let 2*s**2 + 10*s**3 - 5*s**3 - 2*s**5 - 2*s**4 + 2*s**a - 5*s**5 = 0. What is s?
-1, -2/5, 0, 1
Let b(u) be the first derivative of 6*u**5/5 - 8*u**4 + 58*u**3/3 - 20*u**2 + 8*u - 14. Factor b(l).
2*(l - 2)**2*(l - 1)*(3*l - 1)
Let v(z) be the first derivative of -z**6/6 + z**4/2 - z**2/2 - 9. Suppose v(b) = 0. Calculate b.
-1, 0, 1
Let d(k) = k**4 - 6*k**3 - 5*k**2. Let y(p) = 3*p**4 - 13*p**3 - 10*p**2 + p. Let n(z) = 5*d(z) - 2*y(z). Factor n(f).
-f*(f + 1)**2*(f + 2)
Let g(z) = -z**3 - 7*z**2 + 7*z - 3. Let f be g(-8). Suppose 5 = f*w + 2*q, 4*w = q + 13 + 4. Determine i so that 0*i - 2/3 + 0*i**w - 2/3*i**4 + 4/3*i**2 = 0.
-1, 1
Let q(u) = -11*u**2 + 24*u - 46. Let k(l) = 10*l**2 - 25*l + 45. Let n(a) = -6*k(a) - 5*q(a). Factor n(h).
-5*(h - 4)*(h - 2)
Let l be 7/6*27/42*1. Factor 0*q + 3/4*q**4 + 0 + 1/4*q**5 + l*q**3 + 1/4*q**2.
q**2*(q + 1)**3/4
Let y(r) = -r**4 + r**2 - r - 1. Let g(j) = 9*j**4 - 5*j**3 + 4*j + 8. Let k(o) = -5*g(o) - 40*y(o). Find q such that k(q) = 0.
0, 1, 2
Let y = -10 + 14. Factor -3*u**2 + 5*u - 3*u - u - u**y + 3*u**3.
-u*(u - 1)**3
Let i(u) = -u - 1. Let n(r) = -r + 9*r + 12 + 8*r - 2*r + 2*r**2. Let c(a) = -12*i(a) - n(a). Let c(h) = 0. What is h?
-1, 0
Let u(r) be the second derivative of -5*r**7/21 - 16*r**6/45 + r**5/30 + r**4/9 + 41*r. Determine t so that u(t) = 0.
-1, -2/5, 0, 1/3
Suppose 11*a = 8*a - 69. Let w = a + 23. Suppose -10/11*s**3 + 0 + w*s + 24/11*s**4 - 4/11*s**2 = 0. Calculate s.
-1/4, 0, 2/3
Let 0 + 2/11*d - 2/11*d**2 = 0. Calculate d.
0, 1
Determine y, given that 45/4 - 5/4*y**2 + 0*y = 0.
-3, 3
Let v be (4 - 17/5) + 0/1. Factor 9/5*l**3 - 12/5*l**2 + v*l + 0.
3*l*(l - 1)*(3*l - 1)/5
Let u be (-2)/(-7) - (-378)/49. Let s(v) = v**3 - 3*v**2 + 3*v - 1. Let c(b) = -3*b**3 + 9*b**2 - 9*b + 3. Let i(g) = u*s(g) + 3*c(g). Factor i(a).
-(a - 1)**3
Solve -5*z**5 + 7*z + 3*z**5 - 7*z + 2*z**3 = 0.
-1, 0, 1
Factor -6*s**5 - 8*s**3 + 15*s**4 - 14*s**5 + 13*s**4.
-4*s**3*(s - 1)*(5*s - 2)
Let a = 7 - 3. Let t be 0 + 0 - a/(-2). Factor 19*n - 7*n + 8 + 6*n**2 - t*n**3 + 3*n**3.
(n + 2)**3
Let c(r) = 5*r**4 - 16*r**3 + 12*r**2 + 20*r - 13. Let y(f) = 36*f**4 - 111*f**3 + 84*f**2 + 141*f - 90. Let p(q) = -15*c(q) + 2*y(q). Factor p(o).
-3*(o - 5)*(o - 1)**2*(o + 1)
Let j(d) = -6*d**2 - 16*d - 10. Let u = -9 + 6. Let r(c) = 2*c**2 + 5*c + 3. Let b(n) = u*j(n) - 10*r(n). Let b(t) = 0. What is t?
-1, 0
Let p = -245 + 1227/5. Let 0*w**3 + 0*w + 0 - 2/5*w**2 + p*w**4 = 0. What is w?
-1, 0, 1
Suppose -5*r + 6 = -3*v - 5, 5*v - 35 = -5*r. Find w such that -4 - 65*w**2 + 15*w**2 - r - 60*w + 20*w = 0.
-2/5
Let q(i) be the third derivative of 0*i**3 + 6*i**2 + 0 - 2/105*i**7 + 0*i**6 + 0*i + 1/15*i**5 + 0*i**4. Solve q(j) = 0.
-1, 0, 1
Let f(b) = -b**2 - 1. Let a(n) = n - 2. Let t be a(0). Let v(u) = -u**2 - 2*u + 1. Let j be v(t). Let c(r) = -2*r + 6. Let m(q) = j*c(q) + 2*f(q). Factor m(l).
-2*(l - 1)*(l + 2)
Solve 3*y**2 + y**4 + y**2 - y + 2*y**3 - 6*y**2 + 1 - y**5 = 0 for y.
-1, 1
Let b(f) be the third derivative of f**8/3360 - f**7/560 + f**6/240 - f**5/240 - f**3/3 - 3*f**2. Let n(q) be the first derivative of b(q). Factor n(h).
h*(h - 1)**3/2
Let c(v) = 4*v**3 + 2*v**2 - 6*v - 5. Let r(x) = x**3 - x - 1. Let s(q) = c(q) - 5*r(q). Solve s(j) = 0 for j.
0, 1
Suppose 5*w + a - 9 = 0, -3*w + 0*a - 2*a = -4. Suppose 0 = -2*z - 0*z + 4*n + 8, 8 = -3*z - 4*n. Factor z + 0 - s**w.
-s**2
Suppose 30 - 5 = 5*g. Suppose 0 = 3*b - g - 1. Factor -10/3*x + 8/3*x**b + 2/3.
2*(x - 1)*(4*x - 1)/3
Factor -128/7*t**3 - 44*t**4 + 0*t - 16/7*t**2 + 0 - 28*t**5.
-4*t**2*(t + 1)*(7*t + 2)**2/7
Let r = -59/10 - -173/10. Factor 0 + 21/5*s**5 - 3/5*s**2 + 9*s**3 - 6/5*s - r*s**4.
3*s*(s - 1)**3*(7*s + 2)/5
Let g(u) = u**2 + u. Let y(i) be the first derivative of -1 + 0*i - 1/3*i**3 - 1/2*i**2. Let p(q) = 5*g(q) + 3*y(q). What is k in p(k) = 0?
-1, 0
Factor 1/4*p + 0 - p**2.
-p*(4*p - 1)/4
Let q(c) be the first derivative of c**6/40 + c**5/40 - 7*c**4/48 + c**3/12 + c + 2. Let b(i) be the first derivative of q(i). Let b(m) = 0. Calculate m.
-2, 0, 1/3, 1
Suppose -5*s - w = 2*w - 7, 0 = 3*s - w - 7. Suppose 0 + s*u**2 + 2 - 1 - 3 = 0. What is u?
-1, 1
Let d = -9/26 - -11/13. What is s in 1/4*s**4 - 1/4*s**5 - 5/4*s**2 + 0 + d*s + 3/4*s**3 = 0?
-2, 0, 1
Let y(a) = -8*a**2 - 12*a - 4. Let l(v) = 8*v**2 + 13*v + 5. Let w(m) = -2*l(m) - 3*y(m). Factor w(q).
2*(q + 1)*(4*q + 1)
Let w = 44 - 263/6. Let u(a) be the second derivative of -2*a - 1/10*a**5 + 0 - a**2 + 1/3*a**3 + w*a**4. Solve u(g) = 0 for g.
-1, 1
Let x = -2 + 2. Suppose 3*s**3 + x*s**3 - 4*s**3 = 0. Calculate s.
0
Let v(k) be the first derivative of -k**3 - 9*k**2 + 15. Factor v(n).
-3*n*(n + 6)
Let n(k) be the second derivative of -k**6/150 + 3*k**5/50 - 13*k**4/60 + 2*k**3/5 - 2*k**2/5 - 13*k. Let n(u) = 0. What is u?
1, 2
Let j(y) be the first derivative of -5*y**4/14 + 8*y**3/21 + y**2/7 - 19. Determine b, given that j(b) = 0.
-1/5, 0, 1
Factor -2*x + 2/3*x**3 + 0*x**2 + 4/3.
2*(x - 1)**2*(x + 2)/3
Let d(c) be the second derivative of -1/15*c**6 + 1/6*c**4 + 1/21*c**7 + 0 + 0*c**2 - 5*c - 1/10*c**5 + 0*c**3. Factor d(f).
2*f**2*(f - 1)**2*(f + 1)
Let r(s) be the second derivative of s**5/25 - s**4/20 - s**3/20 + s**2/20 + 5*s - 5. Let r(m) = 0. Calculate m.
-1/2, 1/4, 1
Let c(b) be the third derivative of -b**2 - 1/80*b**5 - 1/240*b**6 + 0*b + 1/24*b**3 + 0*b**4 + 0. Solve c(f) = 0 for f.
-1, 1/2
Let x(s) = -s**2 + s. Let t(u) = -3*u**2 - 2*u + 2. Let j(q) = t(q) - 2*x(q). Let o be j(-4). Factor 0 + 2/9*p**3 + 0*p + 2/9*p**o.
2*p**2*(p + 1)/9
Suppose 75 - 85 = -5*n. Factor -1/5 + 0*f + 1/5*f**n.
(f - 1)*(f + 1)/5
Let r(u) be the second derivative of u**5/10 + u**4/6 - 4*u**3/3 - 4*u**2 + 4*u. Factor r(h).
2*(h - 2)*(h + 1)*(h + 2)
Factor -1/2*j**5 - j + 5/2*j**4 + 0 - 9/2*j**3 + 7/2*j**2.
-j*(j - 2)*(j - 1)**3/2
Let m(j) be the second derivative of -1/60*j**4 - 1/15*j**3 - 1/10*j**2 - 2*j + 0. Factor m(b).
-(b + 1)**2/5
Let u(f) be the second derivative of -f**6/135 + f**4/27 - f**2/9 + 5*f. Factor u(j).
-2*(j - 1)**2*(j + 1)**2/9
Let t(w) be the third derivative of w**9/60480 + w**5/30 - 2*w**2. Let o(v) be the third derivative of t(v). Find l such that o(l) = 0.
0
Let v(m) be the third derivative of m**6/180 + m**5/90 - 10*m**2. Let v(u) = 0. Calculate u.
-1, 0
Suppose 5*x = 15, -2*s + 1 - 7 = -4*x. Determine g so that 2*g**4 + s + g**4 - 6*g**2 + 0 = 0.
-1, 1
Let u(j) = -2*j - 2. Let h be u(-3). Factor 0*q + 11*q**2 + h*q + 7*q**2 + 8*q**3.
2*q*(q + 2)*(4*q + 1)
Factor -1/2 + 0*m**2 + m - m**3 + 1/2*m**4.
(m - 1)**3*(m + 1)/2
Let w = 4/49 + 33/196. Let u be ((-2)/(-4))/(4/6). Factor -u*l - 1/4 - 1/2*l**2 + 3/4*l**4 + 1/2*l**3 + w*l**5.
(l - 1)*(l + 1)**4/4
Let t be (-1)/3 - 75/(-63). Let t*q**2 + 6/7*q**3 + 2/7*q + 2/7*q**4 + 0 = 0. Calculate q.
-1, 0
Let r(u) be the second derivative of -1/6*u**4 + 0*u**3 - 3*u + 0*u**2 + 0. Solve r(w) = 0.
0
Suppose -4*t + 20 = d, 8*d - 66 = 4*d - 2*t. Let v be d/(-140)*(-30)/4. Find r such that 2*r**3 + 0 - v*r**2 - 4/7*r + 6/7*r**4 - 10/7*r**5 = 0.
-1, -2/5, 0, 1
Let o(x) be the first derivative of x**5/10 + 7*x**4/6 + 5*x**3 + 9*x**2 + 4*x + 2. Let l(a) be the first derivative of o(a). Factor l(g).
2*(g + 1)*(g + 3)**2
Let q(o) = o**2 - 5*o + 3. Let l be q(4). Let f = l - -4. Factor -2/3*c**2 + 8/9 - 2/