9/60. Let d(g) be the second derivative of -h*g**6 + 0*g**5 + 0 - 3*g + 1/12*g**4 - 1/4*g**2 + 0*g**3. Factor d(k).
-(k - 1)**2*(k + 1)**2/2
Let u(m) be the first derivative of -3*m**4/4 + 9*m**2/2 + 6*m - 7. Factor u(z).
-3*(z - 2)*(z + 1)**2
Let l(w) = 15*w**3 + 2 + 7*w**4 + w**2 - 15*w**3 + 6*w**5 - 4. Let u(q) = 31*q**5 + 35*q**4 - q**3 + 6*q**2 - 11. Let b(k) = -33*l(k) + 6*u(k). Factor b(h).
-3*h**2*(h + 1)**2*(4*h - 1)
Let r(w) be the third derivative of -w**6/200 - w**5/25 - w**4/8 - w**3/5 - 2*w**2. Factor r(z).
-3*(z + 1)**2*(z + 2)/5
Let h = 16/5 + -59/20. Let f(m) be the first derivative of 1 - h*m**4 + 0*m + 1/3*m**3 + 0*m**2. Let f(r) = 0. Calculate r.
0, 1
Let w(b) be the third derivative of -1/108*b**4 - 2*b**2 + 1/135*b**5 + 0*b**3 + 0*b - 1/540*b**6 + 0. Suppose w(j) = 0. Calculate j.
0, 1
Let t(j) be the third derivative of -j**5/15 + j**4/4 + 12*j**2. Factor t(k).
-2*k*(2*k - 3)
Suppose 0 + 3 = -g. Let j be (g - -6) + -4 - -3. Determine w, given that -2/7*w**j - 2/7*w + 0 = 0.
-1, 0
Let j be (0 - 2/(-3)) + 98/42. Factor -s**2 + 1/2*s**4 + s**j + 1/2 - 1/2*s**5 - 1/2*s.
-(s - 1)**3*(s + 1)**2/2
Let p(t) = -t**4 - 6*t**3 + 9*t**2 - 4*t + 6. Let j(a) = a**3 - a**2 + a - 1. Let h(x) = -6*j(x) - p(x). Determine y so that h(y) = 0.
-1, 0, 2
Let s(q) be the second derivative of q**8/3360 + q**7/1260 - q**6/360 - q**5/60 - q**4/4 - q. Let l(p) be the third derivative of s(p). Solve l(g) = 0.
-1, 1
Let s(j) = j**2 - 4*j - 11. Let x be s(7). Let k = x + -8. Find m such that -2/3*m**k + 0 + 2/3*m = 0.
0, 1
Let h(d) = -d**2 + 21*d - 108. Let i be h(10). Suppose 6/7*u**i + 2/7 - 6/7*u - 2/7*u**3 = 0. Calculate u.
1
Let x be (-678)/(-18) - (-4)/3. Let f = -35 + x. Find c, given that -8/3*c**f + 10/3*c**2 - 2/3 - 2*c**3 + 2*c = 0.
-1, 1/4, 1
Suppose -16*k**3 - 8*k**2 - 2622*k**5 - 8*k**2 + 4*k**4 + 2626*k**5 = 0. Calculate k.
-2, -1, 0, 2
Solve 0 + 2*c**2 + c**2 - 2*c + 3 - 4*c**2 = 0 for c.
-3, 1
Let i = -8 + 8. Let t(q) be the first derivative of 0*q + 2/3*q**5 - 7/9*q**6 + i*q**2 + 2 + 0*q**3 + 1/3*q**4. Factor t(w).
-2*w**3*(w - 1)*(7*w + 2)/3
Let v(f) be the first derivative of 0*f - 2/15*f**3 - 2/5*f**2 - 1. Factor v(t).
-2*t*(t + 2)/5
Suppose 3*b + u - 9 = 0, 4*b - 23 = -2*u - 3*u. Suppose -3*f = -2*f. Let f*w**3 + w**3 - w**2 - w**b = 0. What is w?
0, 2
Solve -1/7*c + 0*c**3 + 2/7*c**4 + 0 - 2/7*c**2 + 1/7*c**5 = 0 for c.
-1, 0, 1
Suppose 0 = 4*z - 9*z + 10. Factor -2*v**2 + v**2 - v + 2*v**z.
v*(v - 1)
Suppose 11 = -3*z + 38. Find u, given that u**4 - 6*u**4 + 2 - 2*u**3 - z*u**3 - 10*u - 3*u + 4*u**5 + 23*u**2 = 0.
-2, 1/4, 1
Let x be 3*(-1 + 5)*28/588. Determine i so that -4/7*i**3 + 1/7*i**4 + x*i - 4/7 + 3/7*i**2 = 0.
-1, 1, 2
Solve 3*l - 12*l**2 + 4*l + l**3 - 4*l**4 + 11*l**3 - 3*l = 0.
0, 1
Let k(l) = -l**2 + 6*l + 8. Let d be k(6). Suppose -3 + 27 = d*g. Factor -27/4*o**2 + 23/4*o**g - 7/4*o**4 + 13/4*o - 1/2.
-(o - 1)**3*(7*o - 2)/4
Let b(n) be the first derivative of -1/12*n**4 - 1/6*n + 1/6*n**2 + 0*n**3 + 1/30*n**5 + 4. Factor b(z).
(z - 1)**3*(z + 1)/6
Let j(k) = -k**3 - 26*k**2 + 27*k + 4. Let x be j(-27). Factor 22/7*z**x + 4/7*z**3 + 4*z**5 + 0*z + 0 + 0*z**2.
2*z**3*(2*z + 1)*(7*z + 2)/7
Suppose -3*h + 13 + 4 = 2*d, 4*h - 24 = -4*d. Let z = h - 1. Solve 4 + 2*u**3 + u**4 - 2*u**4 - u**2 - z = 0.
0, 1
Let f(l) be the third derivative of l**5/6 - 35*l**4/48 - 5*l**3/6 - 20*l**2. Determine i, given that f(i) = 0.
-1/4, 2
Let u be 4/(-3) - 80/(-24). Factor 2/3*l + 1/3*l**u + 1/3.
(l + 1)**2/3
Let u = 0 + 1. Suppose -w = -2 - u. Factor 2*y - 2*y**4 - w*y - y**2 + 3*y**4 + y**3.
y*(y - 1)*(y + 1)**2
Let q(v) be the third derivative of -v**10/756000 - 7*v**5/60 - v**2. Let o(w) be the third derivative of q(w). Determine h so that o(h) = 0.
0
Let z(p) be the first derivative of -8*p**6/63 + 4*p**5/15 + 5*p**4/42 - 4*p**3/63 - 13. Determine v so that z(v) = 0.
-1/2, 0, 1/4, 2
Let s(t) = 1 + 2 - t + 2*t**2 + 0 - 2. Let g be s(1). Factor 10/7*x**5 + 0*x + 0 + 2*x**4 + 0*x**g + 4/7*x**3.
2*x**3*(x + 1)*(5*x + 2)/7
Factor 0 - 1/7*x**2 - 3/7*x.
-x*(x + 3)/7
Let g(x) be the first derivative of 2/45*x**3 - 1/30*x**4 + 2/15*x**2 + 0*x - 3. Let g(p) = 0. Calculate p.
-1, 0, 2
Let h(n) = -n**3 - 5*n**2 - 4*n - 3. Let s be h(-4). Let v be 3*s/(-9) + 2. Let -u**3 + u + 2*u**v - 2*u**2 + 4*u**2 = 0. Calculate u.
-1, 0
Solve -8*g + 6*g**3 - 10*g**3 + 6*g**3 = 0 for g.
-2, 0, 2
Let t(d) be the second derivative of d**7/42 - d**6/15 - d**5/10 + d**4/3 + d**3/6 - d**2 + 5*d. Factor t(a).
(a - 2)*(a - 1)**2*(a + 1)**2
Suppose -7*b + 22 = -6. Factor -n**2 + 0 + 1/2*n + 0*n**3 + n**b - 1/2*n**5.
-n*(n - 1)**3*(n + 1)/2
Let q(t) be the first derivative of -t**6/2 + 3*t**5/5 - 15. Factor q(j).
-3*j**4*(j - 1)
Let a(b) be the third derivative of b**5/60 + 7*b**4/72 - b**3/3 - 23*b**2. Find s, given that a(s) = 0.
-3, 2/3
Let y = -7 - -12. Suppose 0*b = -5*b - 5*r + 40, -y*r = -4*b - 4. Suppose 2/3*a**b + 0*a + 0*a**2 + 2/3*a**5 + 0*a**3 + 0 = 0. Calculate a.
-1, 0
Let u(p) = 2*p**2 + 1. Let f be u(-1). Determine q so that 3*q - 2*q - 4*q**4 + 7*q**4 + f*q - 7*q**3 = 0.
-2/3, 0, 1, 2
Factor -4/7*q**4 + 24/7*q**2 + 0*q**3 + 12/7 + 32/7*q.
-4*(q - 3)*(q + 1)**3/7
Let n(a) = -2*a**2 - 8*a + 2. Let f be n(-4). Factor -86/7*x**f - 2/7 + 32/7*x**5 - 16*x**4 + 146/7*x**3 + 22/7*x.
2*(x - 1)**3*(4*x - 1)**2/7
Factor -10/7*v**2 - 26/7*v + 12/7.
-2*(v + 3)*(5*v - 2)/7
Suppose 5 = 2*w + 4*s + 1, 0 = -3*w + s + 6. Solve 4*v**w + 0*v**3 + 4*v**3 - 2*v**2 + 2*v**4 + 0*v**2 = 0.
-1, 0
Factor 0 - 8/3*q**3 + 2/3*q**4 + 2*q**2 + 0*q.
2*q**2*(q - 3)*(q - 1)/3
Let h be 2/13 + (-252)/(-52). Suppose i**2 - 7*i**3 + 3*i**4 + i**4 + h*i**4 + 3*i**4 = 0. What is i?
0, 1/4, 1/3
Let g = 29/4 - 71/12. Factor -g + 2*c - 2/3*c**2.
-2*(c - 2)*(c - 1)/3
Let s = -131/3 - -44. Let n(t) be the first derivative of 0*t - s*t**2 - 1 + 2/9*t**3. Determine i so that n(i) = 0.
0, 1
Suppose 0 = 2*b - 3*n + 6*n, 3*n = 4*b. Solve b*k**2 + 0*k**3 - 3*k**2 + 2*k**3 + k**2 = 0.
0, 1
Let g(n) = n**3 + 6*n**2 - 11*n - 9. Let h be g(-7). Solve 4*q**2 + 29 + 41*q**3 - 112*q**5 - 136*q**4 - h*q + 40*q**2 - 27 = 0 for q.
-1, 1/4, 2/7
Let m(b) be the third derivative of -b**4 + 2*b**3 + 1/4*b**5 - 1/40*b**6 + 0*b + 0 + 3*b**2. Factor m(n).
-3*(n - 2)**2*(n - 1)
Suppose 4*g = -y - 0*y + 14, -4*y + 23 = 5*g. Let r be (-1)/(-4) - (-3)/36. What is t in -r*t**2 - 1/3*t + 1/3*t**4 + 0 + 1/3*t**g = 0?
-1, 0, 1
Let p(f) = -f**2 + 3*f - 6. Let j(c) = -c**2 + 3*c - 7. Let g(t) = -6*j(t) + 7*p(t). Let v(i) = -2*i**2 + 4*i. Let s(q) = 3*g(q) - 2*v(q). Solve s(u) = 0.
-1, 0
Suppose 0*x - w + 8 = x, -2*x + 4*w - 14 = 0. Let c(y) be the first derivative of 0*y - x - 1/5*y**2 + 2/5*y**4 + 2/5*y**3. Factor c(g).
2*g*(g + 1)*(4*g - 1)/5
Let a(n) be the second derivative of -n**9/37800 + n**8/16800 - n**4/6 - 3*n. Let r(z) be the third derivative of a(z). What is h in r(h) = 0?
0, 1
Let g(c) be the third derivative of 0*c**5 + 0*c**3 + 1/112*c**8 + 0*c**4 + 0*c + 5*c**2 + 0 + 1/60*c**6 + 1/42*c**7. Factor g(b).
b**3*(b + 1)*(3*b + 2)
Let z(q) be the second derivative of q**7/7560 - q**5/360 - q**4/6 + 3*q. Let u(m) be the third derivative of z(m). Factor u(c).
(c - 1)*(c + 1)/3
Let k(p) be the third derivative of p**7/735 + p**6/70 + 3*p**5/70 + p**4/21 + 8*p**2. Find i, given that k(i) = 0.
-4, -1, 0
Suppose 0 = 36*y - 49*y. Factor y + 2/11*w**2 - 4/11*w.
2*w*(w - 2)/11
Let z(r) be the second derivative of -r**7/147 + r**5/14 - 4*r**3/21 + 32*r. Let z(x) = 0. What is x?
-2, -1, 0, 1, 2
Let a(l) = 2*l**3 - 35*l**2 + 15*l + 36. Let f be a(17). Suppose -3*t**f - 21/4*t + 3/2 = 0. What is t?
-2, 1/4
Suppose 3*q + 23 = -q + 3*t, 3*q + 13 = -2*t. Let d(k) = k**3 + 6*k**2 + 6*k + 5. Let s be d(q). Factor 1/2*g**3 + s*g**2 - 1/2*g - 1/4*g**4 + 1/4.
-(g - 1)**3*(g + 1)/4
Let s(m) = 10*m**3 + 4*m**2 - 4*m + 4. Let p(t) = -9*t**3 - 5*t**2 + 5*t - 3. Let r(k) = -4*p(k) - 3*s(k). Factor r(j).
2*j*(j + 2)*(3*j - 2)
Suppose -y = -3*m - 10, -5*m + 3*y + 8 - 26 = 0. Let j = 0 - m. Find b, given that 8*b**5 + 2 + 6*b**j + 8*b**4 - 4*b**3 - 2 = 0.
-1/2, 0
Let c be (-2 - -5)*3*(-16)/(-36). Let i(o) be the first derivative of 2*o - 10/3*o**3 - 3 - c*o**2. Let i(j) = 0. What is j?
-1, 1/5
Suppose 0*t = -3*t + 6. Let x be (-49)/(-14)