b(f) be the second derivative of 2*f - 1/38*f**4 - 2/57*f**3 + 0 + 0*f**2. Factor b(i).
-2*i*(3*i + 2)/19
Factor -16/3 - 1/3*l**2 + 8/3*l.
-(l - 4)**2/3
Determine q so that -1/6*q**5 + 5/6*q**3 + 1/2*q**2 + 0 + 0*q + 1/6*q**4 = 0.
-1, 0, 3
Suppose -l - 4*q = -q + 3, 5*q + 10 = 0. Factor -2/3*y**l + 0 - 2/3*y**4 + 2/3*y + 2/3*y**2.
-2*y*(y - 1)*(y + 1)**2/3
Let z = -158 - -161. Find g such that g**z - 4/3 + 4*g - 11/3*g**2 = 0.
2/3, 1, 2
Let b(g) be the second derivative of -50*g**7/7 - 11*g**6/6 + 49*g**5/4 - 5*g**4/3 - 10*g**3/3 - 11*g. Let b(a) = 0. Calculate a.
-1, -1/4, 0, 2/5, 2/3
Let u(t) be the first derivative of -t**6/27 - 2*t**5/45 + t**4/6 + 2*t**3/27 - 2*t**2/9 + 25. Suppose u(r) = 0. Calculate r.
-2, -1, 0, 1
Find s such that 0 + 0*s**2 + 3/5*s**3 - 6/5*s**4 + 0*s + 3/5*s**5 = 0.
0, 1
Factor -1/4*i**2 - 11/8 - 13/8*i.
-(i + 1)*(2*i + 11)/8
Let n(j) be the second derivative of -3*j**5/20 + 13*j**4/30 - 13*j**3/30 + j**2/5 + 21*j. Let n(g) = 0. What is g?
1/3, 2/5, 1
Let 1/6*u**3 + 0 + 0*u - 1/3*u**2 = 0. Calculate u.
0, 2
Determine t, given that 4/7*t**2 + 24/7 - 20/7*t = 0.
2, 3
Let o(y) be the first derivative of 8*y**5/35 - 11*y**4/14 + 6*y**3/7 - y**2/7 - 2*y/7 + 12. Factor o(w).
2*(w - 1)**3*(4*w + 1)/7
Let r(d) be the second derivative of d**6/360 - d**4/24 + 2*d**3/3 + 6*d. Let q(i) be the second derivative of r(i). Factor q(s).
(s - 1)*(s + 1)
Factor -16/13*i - 2/13*i**2 - 32/13.
-2*(i + 4)**2/13
Let a(b) be the second derivative of b**7/105 - b**6/12 + 7*b**5/30 - b**4/4 + 4*b**2 - 3*b. Let q(k) be the first derivative of a(k). What is h in q(h) = 0?
0, 1, 3
Let o(w) = w**2. Let t be o(0). Find u such that u + u + t*u - 3*u + u**2 = 0.
0, 1
Suppose -2*r - 26 - 12 = -5*c, -r = 4. Factor 4*k**3 - 4*k - 77 + 77 - c*k**2.
2*k*(k - 2)*(2*k + 1)
Solve b**2 + 5*b**4 - 96*b**3 - 5*b**2 + 104*b**3 = 0 for b.
-2, 0, 2/5
Let w(f) be the second derivative of f**5/40 - f**4/8 + f**3/4 - f**2/4 + 11*f. Solve w(d) = 0.
1
Let v(w) be the first derivative of -w**7/4620 + w**6/990 - w**5/660 - 7*w**3/3 + 4. Let b(l) be the third derivative of v(l). Suppose b(q) = 0. What is q?
0, 1
Let k(j) be the first derivative of j**5/300 - j**2/2 + 5. Let b(r) be the second derivative of k(r). Factor b(v).
v**2/5
Let g be ((-4)/(-5))/(6/15 - 0). Let k(b) be the first derivative of g*b**2 - 2*b - 2 - 2/3*b**3. Suppose k(o) = 0. What is o?
1
Suppose -1 - 1/2*a**2 + 3/2*a = 0. What is a?
1, 2
Suppose -2*g - 1/2*g**4 + g**3 - 2 + 3/2*g**2 = 0. Calculate g.
-1, 2
Let o(u) be the first derivative of -2/9*u**3 - 2 - 1/18*u**4 - u + 0*u**2. Let f(c) be the first derivative of o(c). Factor f(x).
-2*x*(x + 2)/3
Suppose 0 - 6 = -2*l. Solve -v + 5 + 1 - 6 + v**l = 0 for v.
-1, 0, 1
Let x = -6 - -18. Let h be 3 + (-2 - x/15). Factor h*g - 1/5*g**2 + 1/5*g**4 + 0 - 1/5*g**3.
g*(g - 1)**2*(g + 1)/5
Suppose -3*l + 0 + 0 = 0. Let g(d) be the second derivative of 2/3*d**2 + 3*d - 1/6*d**4 + 1/45*d**6 + 1/30*d**5 - 1/9*d**3 + l. Factor g(w).
2*(w - 1)**2*(w + 1)*(w + 2)/3
Suppose f = -f - 2. Let y be (-3)/(1/f) + 8. Factor -y*j + 2*j**3 + 6*j + 3*j.
2*j*(j - 1)*(j + 1)
Suppose -g + 1 + 2 = 0. Suppose -5*h - 2*m + 15 = -3*m, -m = 5. Factor 4*j**h - 2*j**2 - 5*j**2 + 2*j**4 - 2*j**5 + 2*j**g + j**2.
-2*j**2*(j - 1)**2*(j + 1)
Let b(x) = -3*x**4 + 15*x**3 + 40*x**2 + 12*x - 64. Let f(u) = u**4 - u**3 - u**2 + u. Let c(j) = b(j) + 4*f(j). Factor c(d).
(d - 1)*(d + 4)**3
Suppose 0*p = 4*m + 3*p - 23, p = -3*m + 11. Suppose 1/2*f - 3/2*f**m + 1 + 1/2*f**4 - 1/2*f**3 = 0. Calculate f.
-1, 1, 2
Let q(k) be the second derivative of 0 + 5/24*k**3 - 3/56*k**7 + 1/20*k**5 + 2/15*k**6 - 3/8*k**4 + 1/4*k**2 - 8*k. Find y, given that q(y) = 0.
-1, -2/9, 1
Factor 12*s**3 - 18*s**2 - 3 + 12*s - s**4 - 2*s**4 + 0.
-3*(s - 1)**4
Let x(y) be the second derivative of -y**7/3 - 83*y**6/45 - 33*y**5/10 - 29*y**4/18 + 4*y**3/3 + 4*y**2/3 + 4*y - 2. Find c such that x(c) = 0.
-2, -1, -2/7, 1/3
Factor -6 + 35 + 35*c**2 - 5*c**3 + 11 - 93*c + 23*c.
-5*(c - 4)*(c - 2)*(c - 1)
Let w(a) = -a**3 - 9*a**2 + 11*a + 13. Let r be w(-10). Factor 4*d**3 + 35*d**2 - d**5 - r*d**5 - 4*d**4 - 31*d**2.
-4*d**2*(d - 1)*(d + 1)**2
Suppose 52/7*s**2 + 36/7*s**4 + 0 + 8/7*s + 80/7*s**3 = 0. Calculate s.
-1, -2/9, 0
Let d(v) be the first derivative of 7/16*v**2 + 1/4*v + 1 - 1/6*v**3. Determine t, given that d(t) = 0.
-1/4, 2
Let c be (-4)/(-8)*(0 + 12). Let a(w) = -w**3 + 7*w**2 - 6*w + 4. Let k be a(c). Find r such that 4/3*r**3 - 8/9*r**k + 2/9*r**5 + 2/9*r - 8/9*r**2 + 0 = 0.
0, 1
Let l(d) = -4*d**4 - 7*d**3 + 3*d + 2. Let a(f) = -9*f**2 + 6*f**2 + 4*f - 5*f + 2*f**2 - 1. Let s(v) = 2*a(v) + l(v). Factor s(c).
-c*(c + 1)**2*(4*c - 1)
Let b(v) be the third derivative of -1/40*v**6 + 0*v**3 - 1/70*v**7 + 0*v + 0*v**4 + 0 + v**2 - 1/336*v**8 - 1/60*v**5. Find i, given that b(i) = 0.
-1, 0
Let q = 670 + -668. Let w be 4/(-10)*(-15)/4. Let w + 9/4*m + 3/4*m**q = 0. What is m?
-2, -1
Let u be -2 + (-3 - -3) + 5. Determine k so that 0 + 6/13*k**u - 2/13*k**2 + 0*k = 0.
0, 1/3
Let k(x) be the third derivative of x**9/181440 + x**8/12096 + x**7/1890 + x**6/540 + x**5/15 - 3*x**2. Let i(y) be the third derivative of k(y). Factor i(m).
(m + 1)*(m + 2)**2/3
Let l(k) be the first derivative of k**6/30 + k**5/25 - k**4/20 - k**3/15 + 1. Factor l(h).
h**2*(h - 1)*(h + 1)**2/5
Let w be (-4)/(-6) - 12922/(-210). Let i = w - 62. What is l in -2/5*l**3 - 4/5 + 4/5*l - i*l**4 + 3/5*l**2 = 0?
-2, 1
Suppose 0 = u - 3*k - 16, -4*k + 6*k + 14 = u. Suppose h + h - u = 0. Determine f, given that -f**h - f**5 - 2*f**4 + 2*f**2 - f**3 + 3*f**3 = 0.
-1, 0, 1
Suppose 8 = -7*s + 8*s. Suppose -s = -3*c - c. Factor 6*y**3 - c*y**3 - 2*y**4 + 0*y**3.
-2*y**3*(y - 2)
Let r(q) = q**4 - q**3 - q**2 - q + 1. Let x(m) = -6*m**4 + 4*m**3 + 3*m**2 + 3*m - 3. Let s(a) = 3*r(a) + x(a). Factor s(l).
-l**3*(3*l - 1)
Let y(h) be the first derivative of -h**5/35 + 2*h**3/21 - h/7 + 9. Factor y(z).
-(z - 1)**2*(z + 1)**2/7
Let h(k) be the third derivative of 2*k**7/105 - k**6/15 + k**5/15 - 8*k**2. Let h(x) = 0. What is x?
0, 1
Let z = -11 + 15. Find r, given that -9*r**z + 12*r**2 + 8*r**3 + 2*r**4 - 2*r**4 + 4*r**3 = 0.
-2/3, 0, 2
Let f be (1/(-2))/(2/(-8)). Determine w, given that 2*w**5 + 2 + 6*w + 2*w + 20*w**2 + 10*w**4 + 20*w**3 + f*w = 0.
-1
Factor 4*s**3 - 4 + 3 - 30*s - 2*s**3 + s**4 + 28*s.
(s - 1)*(s + 1)**3
Let s(k) be the third derivative of k**8/20160 - k**6/720 + k**5/20 + k**2. Let u(m) be the third derivative of s(m). Factor u(h).
(h - 1)*(h + 1)
Let j be (0 - 5) + (-64)/(-8). Let s(o) be the second derivative of 1/8*o**j + 3/16*o**4 + 9/80*o**5 + 0 + 1/40*o**6 - 2*o + 0*o**2. Factor s(a).
3*a*(a + 1)**3/4
Let r be -4*(-2)/(-4) + 4. Let m(j) be the first derivative of 2/3*j**3 - 1/5*j**5 - j - 1/2*j**2 + 1/2*j**4 - 1/6*j**6 + r. Factor m(p).
-(p - 1)**2*(p + 1)**3
Suppose 0 = d - 2 - 0. Suppose 4*k - 26 = -d. Factor t**4 + k*t**3 + 12*t + 0*t**4 + 13*t**2 + 3*t**4 + 4 - 3*t**4.
(t + 1)**2*(t + 2)**2
Let k(n) = -n - 2. Let h be k(-5). Let b(x) be the first derivative of -2 + 1/7*x**2 + 4/7*x - 13/14*x**4 - 2/7*x**5 - 6/7*x**h. Factor b(m).
-2*(m + 1)**3*(5*m - 2)/7
Find m, given that -1/3*m**2 - 1 + 4/3*m = 0.
1, 3
Let w = -3/91 - -191/273. Factor w*q**2 + 8/3*q + 8/3.
2*(q + 2)**2/3
Let g be 5 - (-2)/3*77/(-22). Suppose -g*x**4 + 0 - 4*x**2 + 6*x**3 + 2/3*x = 0. What is x?
0, 1/4, 1
Let g(f) = 8*f**2 - 90*f + 402. Let h(u) = 15*u**2 - 180*u + 805. Let r(y) = 5*g(y) - 3*h(y). Factor r(q).
-5*(q - 9)**2
Let x(a) be the first derivative of -5*a**6/6 - 3*a**5 - 5*a**4/2 + 10*a**3/3 + 15*a**2/2 + 5*a - 16. Let x(b) = 0. What is b?
-1, 1
Let t(z) be the third derivative of z**4/24 - 7*z**3/6 + 3*z**2. Let i be t(9). Factor 1/3*g + 4/3*g**4 + 1/3*g**5 + 0 + i*g**3 + 4/3*g**2.
g*(g + 1)**4/3
Let u(m) = -7*m**3 + 27*m**2 - 3*m + 3. Let j(b) = 22*b**3 - 82*b**2 + 10*b - 10. Let a(x) = 3*j(x) + 10*u(x). Factor a(l).
-4*l**2*(l - 6)
Let s(l) be the first derivative of -1/2*l**4 - 7*l**2 - 6*l - 3 - 10/3*l**3. Suppose s(p) = 0. Calculate p.
-3, -1
Let f(v) = -6*v**3 - 4*v**2 + 6*v. Let z(s) = -6*s**2 + 7*s + s**2 + 0*s**3 - s**3 - 6*s**3. Let g = 6 - 1. Let x(n) = g*f(n) - 4*z(n). Let x(c) = 0. What is c?
-1, 0, 1
Let z(u) be the third derivative of