 = -22*g**2 + 32*g - 12. Let m(t) be the third derivative of 3*t**5/20 - 13*t**4/24 + 5*t**3/6 - 4*t**2. Let i(k) = 12*m(k) + 5*q(k). Factor i(f).
-2*f*(f - 2)
Suppose -2*n + 28 = 2*n. Let s(t) be the third derivative of 0*t**4 - 1/3*t**3 - t**2 + 0 + 1/15*t**5 + 0*t + 0*t**6 - 1/105*t**n. Factor s(x).
-2*(x - 1)**2*(x + 1)**2
What is h in 1/2*h**3 + 3/2*h**2 + 1/2 + 3/2*h = 0?
-1
Suppose 0 = 2*n - 0 - 4. Suppose 0 = -2*a - n*a + 8. Solve -3*t**3 - 9*t + 7 - 3*t**a - 4 + 12*t**2 = 0 for t.
1
Let b(q) = 4*q**2 + 4*q. Let m(n) = -13*n**2 - 13*n. Let f(h) = 7*b(h) + 2*m(h). Factor f(y).
2*y*(y + 1)
Let m(s) be the first derivative of -2*s**5/45 + 2*s**3/27 - 3. Solve m(i) = 0 for i.
-1, 0, 1
Let i = 16 - 14. Factor 2/5*r**i + 4/5*r + 2/5.
2*(r + 1)**2/5
Let q(l) be the third derivative of -l**5/450 + l**4/180 + 7*l**2. Solve q(h) = 0.
0, 1
Suppose -136 = 8*h - 168. Factor -33/4*b**3 + 0 - 5/2*b**2 - 1/4*b - h*b**5 - 10*b**4.
-b*(b + 1)**2*(4*b + 1)**2/4
Let t(j) be the first derivative of 1/10*j**2 + 1/50*j**5 + 2 - 1/15*j**3 + 2*j - 1/150*j**6 + 0*j**4. Let h(u) be the first derivative of t(u). Factor h(v).
-(v - 1)**3*(v + 1)/5
Determine f, given that -64*f**2 + 0*f - 2 - 32*f - 2 = 0.
-1/4
Let s(u) be the first derivative of -u**5/15 - u**4/12 + 2*u**3/9 + 34. What is x in s(x) = 0?
-2, 0, 1
Let h(x) be the first derivative of -2*x**6/3 - 12*x**5/5 - x**4 + 4*x**3 + 4*x**2 + 15. Find q such that h(q) = 0.
-2, -1, 0, 1
Suppose 4*r = -4*l + r - 15, 0 = -4*l + 5*r + 25. Factor 0*n**3 + l + 0*n + 2/5*n**4 - 2/5*n**2.
2*n**2*(n - 1)*(n + 1)/5
Determine u so that -778*u - u**3 + u**5 + 778*u = 0.
-1, 0, 1
Let q(k) be the second derivative of k**8/30240 - k**4/12 + 2*k. Let l(i) be the third derivative of q(i). Factor l(g).
2*g**3/9
Let f = -2 - -7. Let u(c) = c. Let w be u(2). Factor -n**w - n**3 + 2*n**2 - 2*n**4 + n**f + n**4.
n**2*(n - 1)**2*(n + 1)
Let o(b) be the third derivative of -b**7/630 - b**6/180 + b**5/15 + b**4/6 - 3*b**2. Let p(q) be the second derivative of o(q). Factor p(d).
-4*(d - 1)*(d + 2)
Suppose -3*l + 5 = -1. Factor -9 + 2*z**2 - z**3 + l*z + 11 - 4 - z.
-(z - 2)*(z - 1)*(z + 1)
Let k(x) = -x - 1. Let u be k(-4). Let o = 5 + -2. Find j such that -j**2 + u - o - j = 0.
-1, 0
Let w be -5 - -3 - (-4 - 0). Factor 5*z - 2*z**3 - 11*z - z**2 - 2 - 3*z**w - 2*z**2.
-2*(z + 1)**3
Let s = -15 - -8. Let w(m) = -m**2 - 4*m - 3. Let z(i) = -3*i**2 - 13*i - 10. Let b(h) = s*w(h) + 2*z(h). Factor b(g).
(g + 1)**2
Let q(y) = 17*y**4 - 40*y**3 + 55*y**2 - 23*y - 9. Let s(c) = 8*c**4 - 20*c**3 + 28*c**2 - 12*c - 4. Let o(r) = -4*q(r) + 9*s(r). Suppose o(d) = 0. Calculate d.
0, 1, 2
Determine s so that 23*s**2 + 18*s**2 + 112*s**5 - 13*s**2 + 206*s**3 + 276*s**4 - 18*s - 4 = 0.
-1, -1/2, -1/4, 2/7
Let y(l) = l - 6. Suppose -9 = 3*m - 4*m. Let w be y(m). Factor -c**4 - 2 + 5*c + 0*c**3 + 5*c**4 - c**5 + c**3 - 2*c**2 - 5*c**w.
-(c - 2)*(c - 1)**3*(c + 1)
Let p(b) = 7*b + 1. Let x be p(2). Let j be -3*(-5)/(x/4). Factor -4*h + j*h**3 + 6*h - 3*h**3 - 3*h.
h*(h - 1)*(h + 1)
Let j(d) be the second derivative of -d**7/4620 - d**6/660 - d**5/330 + d**3/3 - 4*d. Let r(t) be the second derivative of j(t). What is q in r(q) = 0?
-2, -1, 0
Let c(q) be the second derivative of -3*q**5/20 + 3*q**4/4 + 2*q**3 - 22*q. Let c(g) = 0. What is g?
-1, 0, 4
Suppose 0 = -3*g - 15, -2*g = -4*z + 1 + 9. Determine a, given that -2/13*a**2 + z + 0*a + 4/13*a**3 - 2/13*a**4 = 0.
0, 1
Suppose -q = 4*q - 15. Factor -2*l**2 + 5*l**2 - 6*l**2 + 2*l**q + l**2.
2*l**2*(l - 1)
Let x(o) be the first derivative of -1/9*o**6 - 8/15*o**5 + 4/3*o - 2/3*o**4 + 5/3*o**2 + 4/9*o**3 - 2. Determine t, given that x(t) = 0.
-2, -1, 1
Let c(d) = d**3 + 2*d**2 - 2*d - 2. Let t be (6/(-4))/((-3)/(-4)). Let z be c(t). Factor -z*x**2 + 6 - 2*x - 6.
-2*x*(x + 1)
Let z be (-1 + 3/2)*6. Factor q + 6*q**4 + q - z*q**2 + 3*q**4 - 8*q**4.
q*(q - 1)**2*(q + 2)
Let q(f) = -57*f**3 + 25*f**2 + 21*f + 11. Let s(y) = 28*y**3 - 12*y**2 - 10*y - 6. Let u(h) = -4*q(h) - 7*s(h). Suppose u(m) = 0. What is m?
-1/4, 1
Let c(y) be the third derivative of y**9/241920 - y**8/40320 + y**7/20160 - y**5/15 - 4*y**2. Let z(t) be the third derivative of c(t). Factor z(h).
h*(h - 1)**2/4
Let k = 11 + -9. Let i(c) be the first derivative of 2/7*c - 32/35*c**5 + 8/7*c**2 - k - 4/7*c**4 + 10/7*c**3. What is u in i(u) = 0?
-1, -1/4, 1
Factor -9*i**2 + 13*i - 45*i + 64 + 13*i**2.
4*(i - 4)**2
Let h(s) be the first derivative of s**6/180 + s**5/30 + s**4/12 - 4*s**3/3 - 3. Let l(p) be the third derivative of h(p). Factor l(r).
2*(r + 1)**2
Let g(b) be the first derivative of -3*b**6/10 + 3*b**5/10 - b**4/12 + 4*b - 4. Let c(a) be the first derivative of g(a). Suppose c(d) = 0. What is d?
0, 1/3
Let b(f) = 3*f - 22. Let a(p) = -2*p + 15. Let v(y) = 7*a(y) + 5*b(y). Let l be v(7). Factor 2/7*h**3 + 2/7 - 2/7*h**l - 2/7*h.
2*(h - 1)**2*(h + 1)/7
Let k(t) be the first derivative of 4*t**3/3 - 2*t**2 + 7. Solve k(i) = 0 for i.
0, 1
Let -95*c**3 + 3 + 9 - 10*c**2 - 4*c + 99*c**3 - 2*c**2 = 0. Calculate c.
-1, 1, 3
Let j(t) be the third derivative of -t**8/20160 + t**6/720 + t**5/60 - 5*t**2. Let f(q) be the third derivative of j(q). Determine o so that f(o) = 0.
-1, 1
Let s(t) = 4*t**3 + t - 1. Let f be s(1). Suppose 0 = -f*k - 0 + 8. Factor 4*m + 2*m**2 + k*m**3 - 44*m**3 + 0*m**3.
-2*m*(3*m - 1)*(7*m + 2)
Let i(g) be the third derivative of g**6/120 - g**5/15 + g**4/6 - 36*g**2. Let i(a) = 0. Calculate a.
0, 2
Suppose 2*i + 3*i - 15 = 0. What is c in -2*c**2 + 2*c**3 + 4*c**3 + 2*c**i = 0?
0, 1/4
Let f(i) be the first derivative of 4*i**5/5 - 10*i**4 + 44*i**3 - 80*i**2 + 64*i - 25. Factor f(y).
4*(y - 4)**2*(y - 1)**2
Suppose 5*p - 4 - 1 = 0. Let c be -1 + 2 + p + 1. Factor 1 - 1 + j**c.
j**3
Solve -3*k**2 - 3 - 9*k**3 - k + 6*k**4 - k + 11*k = 0.
-1, 1/2, 1
Let 3*z**4 - 5*z**4 + 10*z + 123*z**3 + 2*z**2 - 133*z**3 = 0. What is z?
-5, -1, 0, 1
Let l(d) be the third derivative of d**8/84 + 2*d**7/35 - 4*d**5/15 - 10*d**2. Solve l(x) = 0.
-2, 0, 1
Let l(z) = -z**3 + 2*z + 2. Let p be l(-2). Let r = p - 2. Solve 3 - 4 + 0*g**2 + 3*g + r*g**2 = 0.
-1, 1/4
Suppose 2*k + 3*k = 25. Let t be (7 - k)/((-2)/(-3)). Solve 2/3*f**t - 2/3*f**2 + 0 + 2/9*f - 2/9*f**4 = 0 for f.
0, 1
Let g = 19 + -15. Let d(h) be the third derivative of -1/21*h**3 + 0 + 0*h**g + 2*h**2 + 1/210*h**5 + 0*h. Determine u so that d(u) = 0.
-1, 1
Let h(x) be the third derivative of -x**5/20 + x**4/8 + 3*x**3 + 14*x**2. Factor h(p).
-3*(p - 3)*(p + 2)
Let k(u) be the second derivative of -3*u**5/20 + 3*u**4/4 - 3*u**3/2 + 3*u**2/2 + 2*u. Determine f so that k(f) = 0.
1
Let x(v) = 6*v - 12. Let j be x(8). Suppose -c**3 - 32*c**2 - 7*c**3 - 4 - 12*c**5 + 8*c + 16*c + j*c**4 - 4*c**5 = 0. What is c?
-1, 1/4, 1
Let n(a) = a**2 - 6*a + 5. Let w(p) = -2. Let z(o) = 2*n(o) - 4*w(o). Factor z(c).
2*(c - 3)**2
Solve 0 + 4/3*v + 4/9*v**3 + 16/9*v**2 = 0.
-3, -1, 0
Let i = -78 - -78. Let m(p) be the second derivative of p - 1/21*p**4 + i + 0*p**2 - 3/70*p**5 + 1/21*p**3. What is c in m(c) = 0?
-1, 0, 1/3
Let j = 7 + -13. Let t(g) = 7*g**2 - 4*g + 10. Let i(p) = -13*p**2 + 8*p - 19. Let n(c) = j*i(c) - 11*t(c). Factor n(a).
(a - 2)**2
Solve 1904 + 28*c**5 - 1904 + 44*c**3 - 64*c**4 + 0*c**2 - 8*c**2 = 0 for c.
0, 2/7, 1
Let y(u) be the second derivative of 1/5*u**2 + 0 + 1/30*u**4 + 2/15*u**3 + 2*u. Factor y(v).
2*(v + 1)**2/5
Suppose 6*t - t = 30. Find p such that t*p - 2 - 72*p**4 - 3*p + 31*p**3 + 22*p**2 - 7*p - 7*p**3 = 0.
-1/3, 1/2
Let s(r) be the second derivative of -r**5/30 - r**4/18 + 2*r**3/9 + 4*r. Suppose s(z) = 0. Calculate z.
-2, 0, 1
Let k = -117/2 + 60. Factor 3/2*b**4 + 0 + 0*b**2 + 0*b + k*b**3.
3*b**3*(b + 1)/2
Factor 114 + 8*a**2 + 2*a - 114 - 4*a.
2*a*(4*a - 1)
Let v(n) be the first derivative of -3*n**4/28 - 3*n**3/7 - 3*n**2/7 + 6. Factor v(p).
-3*p*(p + 1)*(p + 2)/7
Let d(w) be the second derivative of 2/3*w**2 + w + 1/18*w**4 + 0 - 1/3*w**3. Factor d(f).
2*(f - 2)*(f - 1)/3
Solve -2 + 4 - c - 97*c**2 - 8*c + 101*c**2 = 0 for c.
1/4, 2
Let o(z) be the second derivative of z**4/4 - 10*z**3 + 150*z**2 + 13*z. Suppose o(n) = 0. Calculate n.
10
Let d(x) = 3*x**4 - 2*x**3 - 8*x**2 - 4*x + 1. Let c(t) = -t**3 + 1. Let h(s) = -c(s) + d(s). Factor h(i).
i*(