 = -z**2 + 1. Let k(m) = -8*m**2 + 25*m + 3. Let l(r) = -k(r) + 3*n(r). Factor l(q).
5*q*(q - 5)
Suppose 0 = -4*d - 0*d - 20, 2*d = 2*q - 16. Let w = 5 - q. Suppose 0*c**w + 2/5*c**3 - 2/5*c + 0 = 0. Calculate c.
-1, 0, 1
Let w(r) be the first derivative of -r**5/180 + r**4/72 + 2*r**2 - 5. Let a(i) be the second derivative of w(i). What is s in a(s) = 0?
0, 1
Let r(s) = 3*s + 36. Let u be r(-12). Find y such that -1/3*y - 1/3*y**2 + u = 0.
-1, 0
Let f(t) be the third derivative of -4*t**2 + 1/15*t**3 + 0*t - 1/40*t**4 + 1/300*t**5 + 0. Solve f(v) = 0.
1, 2
Factor 0 - 2/9*d - 2/9*d**3 + 4/9*d**2.
-2*d*(d - 1)**2/9
Let o(j) be the second derivative of -j**6/60 - j**5/15 + j**4/12 + 2*j**3/3 - 2*j**2 + j. Let g(q) be the first derivative of o(q). Solve g(m) = 0.
-2, -1, 1
Let b(c) be the third derivative of -1/8*c**4 + 1/10*c**5 - 1/2*c**3 + 1/20*c**6 - 1/112*c**8 - 1/70*c**7 + 0 + 2*c**2 + 0*c. Let b(j) = 0. What is j?
-1, 1
Let h(l) = l - 5. Let f be h(8). Suppose 25 = 5*s - 0*s. Factor -a**4 + a**2 + a**3 - s*a**f + 4*a**3.
-a**2*(a - 1)*(a + 1)
Let v(s) be the first derivative of -s**5/450 + s**2/2 + 11. Let j(x) be the second derivative of v(x). Factor j(o).
-2*o**2/15
Factor 320*b - 4 - 12 - 300*b - 4*b**2.
-4*(b - 4)*(b - 1)
Let s(v) be the second derivative of v**7/42 - v**6/10 + v**5/20 + v**4/4 - v**3/3 - 2*v. Factor s(u).
u*(u - 2)*(u - 1)**2*(u + 1)
Solve 0 + 8/19*c**2 + 0*c + 2/19*c**3 = 0 for c.
-4, 0
Factor 1/2 - 1/2*j**2 + 0*j.
-(j - 1)*(j + 1)/2
Let k(x) be the third derivative of -x**8/168 - x**7/105 + x**6/30 - 66*x**2 + 2. Factor k(w).
-2*w**3*(w - 1)*(w + 2)
Let j(u) be the second derivative of -5*u**7/14 - u**6/6 + 21*u**5/4 + 125*u**4/12 + 5*u**3 - 27*u. Solve j(b) = 0.
-2, -1, -1/3, 0, 3
Determine n, given that 0*n**2 + 3/2*n**3 - 3/2*n**4 + 0*n + 0 = 0.
0, 1
Let a(h) be the first derivative of 0*h + 1/2*h**6 + 0*h**2 + 3/5*h**5 + 6 + 0*h**3 + 0*h**4. Factor a(o).
3*o**4*(o + 1)
Let x(q) be the first derivative of q**8/5040 + q**7/2520 - q**6/360 - q**5/360 + q**4/36 - 2*q**3/3 - 4. Let m(z) be the third derivative of x(z). Factor m(t).
(t - 1)**2*(t + 1)*(t + 2)/3
Let k(r) be the second derivative of r**4/6 + r**3/3 - 2*r**2 - 9*r. Factor k(i).
2*(i - 1)*(i + 2)
Let p = -204 - -6121/30. Let w(a) be the second derivative of 2/3*a**2 + 3*a + 0 + 1/9*a**3 - 1/9*a**4 - p*a**5. Find b, given that w(b) = 0.
-2, -1, 1
Let -9/2*n**2 - 6*n - n**3 - 2 = 0. Calculate n.
-2, -1/2
Let s(z) be the second derivative of -z**5/2 + 15*z**4/8 - 5*z**3/2 + 5*z**2/4 - 15*z. Factor s(c).
-5*(c - 1)**2*(4*c - 1)/2
Let k = 10 - 5. Let t(c) be the second derivative of 0*c**2 + 0 + 1/3*c**3 - 9/20*c**k + 1/6*c**6 + 3*c + 1/6*c**7 - 5/12*c**4. Factor t(q).
q*(q - 1)*(q + 1)**2*(7*q - 2)
Let a be 112/132 - (-8)/(-12). Factor 0*z + 0 + 0*z**2 + 2/11*z**3 - a*z**4.
-2*z**3*(z - 1)/11
Let b(c) be the third derivative of 1/144*c**4 + 0*c + 9*c**2 + 0 + 1/360*c**5 - 1/18*c**3. Factor b(n).
(n - 1)*(n + 2)/6
Let o(y) be the third derivative of y**5/390 + y**4/156 - 2*y**3/39 - 9*y**2. Let o(r) = 0. What is r?
-2, 1
Suppose 0*l**2 + 1/8 - 1/8*l**4 + 1/4*l**3 - 1/4*l = 0. What is l?
-1, 1
Let n(h) = h**5 + 5*h**4 - 2*h**3 - 5*h**2 - 4*h. Let l(z) = -z**5 + z**3 + z. Let f(m) = 15*l(m) + 3*n(m). Find a such that f(a) = 0.
-1, 0, 1/4, 1
Let -3/2*t**5 + 2*t**3 + 0*t - 2*t**2 + 0 + 5/2*t**4 = 0. What is t?
-1, 0, 2/3, 2
Let z = -3 - -5. Let d be (-3)/(-6) + 1/(-4). Let -d*m**4 + 0*m - 1/4*m**5 + 0 + 1/4*m**3 + 1/4*m**z = 0. What is m?
-1, 0, 1
Let h(d) be the first derivative of 98*d**5/15 - 77*d**4/6 + 64*d**3/9 - 4*d**2/3 + 9. Determine y, given that h(y) = 0.
0, 2/7, 1
Let y(a) be the first derivative of 2/25*a**5 + 7/30*a**6 + 0*a + 0*a**2 - 2/15*a**3 - 1 - 7/20*a**4. Suppose y(x) = 0. Calculate x.
-1, -2/7, 0, 1
Let s(u) = 51*u**3 - 4*u**2 + 3*u. Let t be s(2). Let i = t - 3578/9. What is f in i*f**2 + 0 - 2/9*f = 0?
0, 1/2
Let y(x) be the second derivative of -x**6/3 - 76*x**5/5 - 260*x**4 - 5600*x**3/3 - 2000*x**2 + 52*x. Solve y(f) = 0 for f.
-10, -2/5
Let x(g) be the first derivative of g**4/20 - 3*g**2/10 - g + 7. Let f(r) be the first derivative of x(r). Factor f(i).
3*(i - 1)*(i + 1)/5
Let z(h) = h + 10. Let m be z(-7). Find s such that 0*s + 3/7*s**4 + 0 - 3/7*s**m - 1/7*s**5 + 1/7*s**2 = 0.
0, 1
Let j be 4/(-6) - (-24)/36. Let q(x) be the second derivative of -3*x - 1/5*x**5 - 2/3*x**3 + 1/2*x**4 + 1/2*x**2 + j + 1/30*x**6. Factor q(v).
(v - 1)**4
Let m(s) = 10*s**2 - 46*s + 4. Let i(a) = 2*a**2 - 9*a + 1. Let y(b) = 16*i(b) - 3*m(b). Find u, given that y(u) = 0.
1, 2
Let u(z) be the first derivative of -z**6/15 + 2*z**4/5 + 4*z**3/15 - 3*z**2/5 - 4*z/5 - 13. Suppose u(o) = 0. Calculate o.
-1, 1, 2
Suppose -2/3 - 1/3*g**3 + 1/3*g**4 + 5/3*g - g**2 = 0. What is g?
-2, 1
Let y = 1 + -5/6. Let d(o) be the first derivative of 0*o + y*o**2 - 2 - 1/9*o**3. Factor d(n).
-n*(n - 1)/3
Let f(d) be the second derivative of -3*d**5/20 - 3*d**4/4 + 6*d**2 + 11*d. Factor f(t).
-3*(t - 1)*(t + 2)**2
Let u(i) = -3*i + 3. Suppose 0 = 4*x - 5*x + 7. Let r(b) = -2 - 6 - b**2 - b + x. Let k(s) = -3*r(s) - u(s). Factor k(h).
3*h*(h + 2)
Let m(c) be the second derivative of -c**6/120 + c**5/80 + 7*c**4/48 - c**3/24 - 3*c**2/4 + 42*c. Determine y, given that m(y) = 0.
-2, -1, 1, 3
Let b(n) = 3*n**3 - 3*n**2 - 27*n + 27. Let c(i) = -3*i**3 + 3*i**2 + 27*i - 27. Let u(w) = -2*b(w) - 3*c(w). Determine s, given that u(s) = 0.
-3, 1, 3
Suppose w + 52 = 5*w. Factor 3*j**4 + 0*j**4 + j - 4*j**3 + 2*j + 9*j**2 + w*j**3.
3*j*(j + 1)**3
Let o(y) = -y**3 + 2*y**2 + 6*y - 2. Let i be 1 + (-1 + 3)*2. Let g(z) = z**3 - 2*z**2 - 5*z + 2. Let b(j) = i*g(j) + 4*o(j). What is a in b(a) = 0?
-1, 1, 2
Let v = -17 + 19. Let a(z) = -13*z**2 + z. Let h(o) = 6*o**2 + 0*o**2 - 3*o**2. Let p(k) = v*a(k) + 9*h(k). Factor p(d).
d*(d + 2)
Let l be ((-2)/(-4))/((-1)/(-10)). Let -28*o**4 - 49*o**l + 2 - 4*o**3 + 0 - 2 = 0. Calculate o.
-2/7, 0
Let a be -2*(-2)/8 + (-49)/140. Let d(k) be the first derivative of 2 + 0*k**2 + 1/24*k**6 - 1/12*k**3 + 0*k + 3/16*k**4 - a*k**5. Determine t so that d(t) = 0.
0, 1
Let c(h) be the third derivative of 1/420*h**6 + 0*h**3 + 0*h + 2*h**2 + 0 + 0*h**4 - 1/210*h**5. Factor c(n).
2*n**2*(n - 1)/7
Suppose 2*u + l = -3*l, -3*u + 30 = -4*l. Let k be 10/u + 3/9. Let 0*g**2 - 3*g**2 + 2*g**k - 3*g - 2 = 0. What is g?
-2, -1
Let u(r) be the first derivative of r**5/80 + r**4/24 + r**3/24 - r - 3. Let b(o) be the first derivative of u(o). Factor b(y).
y*(y + 1)**2/4
Let m be (-72)/(-40) + 1/5. Let o(z) be the first derivative of -1/22*z**4 - 12/11*z**2 - 16/11*z - 4/11*z**3 + m. Factor o(g).
-2*(g + 2)**3/11
Solve 0*j + 2/5*j**3 + 0 + 0*j**2 + 7/5*j**4 = 0 for j.
-2/7, 0
Let d(q) = 24*q**4 + 31*q**3 - 47*q**2 - 53*q + 23. Let t(s) = 8*s**4 + 10*s**3 - 16*s**2 - 18*s + 8. Let g(z) = -4*d(z) + 11*t(z). What is o in g(o) = 0?
-2, -1, 1/4, 1
Suppose -p - p - 5*z + 14 = 0, 5*p + z = 12. Factor 0*j**2 - 3*j**p - 2*j**3 + j**3 + 4*j**2.
-j**2*(j - 1)
Suppose -707*z = -718*z + 44. Factor -5/2*w**2 - z*w - 2 - 1/2*w**3.
-(w + 1)*(w + 2)**2/2
Suppose -3*n + 7*n = 0. Let l(v) be the second derivative of 0*v**5 + n + 0*v**2 + v + 1/30*v**6 + 0*v**3 - 1/12*v**4. Determine g so that l(g) = 0.
-1, 0, 1
Let g(b) be the second derivative of 0*b**3 - 2/3*b**4 - 7*b + 0 - 2/5*b**5 + 0*b**2 - 1/15*b**6. Factor g(v).
-2*v**2*(v + 2)**2
Suppose -t + 10*t = -3*t. Factor 2/9*b + 2/9*b**2 + t.
2*b*(b + 1)/9
Let u(r) be the third derivative of r**8/40320 + r**7/5040 + r**6/1440 - r**5/30 + r**2. Let v(a) be the third derivative of u(a). Factor v(f).
(f + 1)**2/2
Let c(l) be the third derivative of l**6/720 + l**5/120 - l**3/9 + l**2. Find j, given that c(j) = 0.
-2, 1
Solve -8/3*n - 4/3*n**5 + 4/3*n**4 + 0 + 4*n**3 - 4/3*n**2 = 0.
-1, 0, 1, 2
Let j(c) = c**3 - 10*c**2 - 10*c - 11. Let n be j(11). Let f(x) be the first derivative of 3 + n*x**2 + 0*x + 2/21*x**3. Factor f(l).
2*l**2/7
Let o = -50152130/4257 + 129594/11. Let v = o - -2/43. Let 4/9*f**3 + 0 + 0*f - v*f**2 - 2/9*f**4 = 0. What is f?
0, 1
Let s(w) be the first derivative of -w**7/135 + w**6/60 - w**5/135 - 3*w**2/2 - 2. Let d(o) be the second derivative of s(o). Factor d(p).
-2*p**2*(p - 1)*(7*p - 2)/9
Let t(x) = x**2 + 8*x + 2. L