4*k - 3*k**2 = 0.
-3, -1
Let x = 14 - 12. Find a, given that 15/2*a**2 + x + 25/4*a**3 - 9*a = 0.
-2, 2/5
Let b = 25 + -33. Let l be (-12)/b + 3/2. Factor 1/4*n**4 + 3/4*n**l + 0*n**2 - n + 0.
n*(n - 1)*(n + 2)**2/4
Let g(q) = q**2 - 1. Let z(i) = 14*i**3 - 13*i**2 - 32*i - 5. Let s(v) = 3*g(v) + z(v). Factor s(c).
2*(c - 2)*(c + 1)*(7*c + 2)
Suppose -19*n = -10*n. Let a(c) be the second derivative of 0 - 1/24*c**3 + 1/24*c**4 - 1/80*c**5 + n*c**2 - c. Solve a(w) = 0.
0, 1
Let o = 50 - 48. Let h(w) be the second derivative of -1/6*w**4 + 3/7*w**3 - w + 0 - 2/7*w**o. Find p such that h(p) = 0.
2/7, 1
Let f(a) be the first derivative of a**7/105 - a**6/30 + a**5/30 - 3*a**2 - 5. Let m(o) be the second derivative of f(o). Determine j so that m(j) = 0.
0, 1
Suppose 4*w - 2*d = 20, w + 2 = -0*w - 3*d. Determine y, given that -25*y - 14 - w + 10*y**2 - 2*y**3 + 19*y = 0.
-1, 3
Suppose 5*d - 5 = 3*p, d = 3*p - 6*p + 19. Factor -4/7*j**2 + 0 + 4/7*j**4 + 0*j**3 - 2/7*j + 2/7*j**p.
2*j*(j - 1)*(j + 1)**3/7
Let w(s) = -2 - 4*s**2 + 5 - 5*s**3 + 1 + 5*s. Let i(n) = 4*n**3 + 3*n**2 - 4*n - 3. Let r(z) = -4*i(z) - 3*w(z). Factor r(q).
-q*(q - 1)*(q + 1)
Let t(u) be the third derivative of -u**5/240 - u**4/24 - u**3/6 - 10*u**2. Suppose t(r) = 0. Calculate r.
-2
Suppose -g + 2*i + 6 = -3*g, 5*i = 2*g - 29. Factor -4*c**2 - c**4 - g*c**4 + 4*c**5 - 8*c**3 - 5*c**5 - 2*c**4.
-c**2*(c + 1)*(c + 2)**2
Let y = -1 - -1. Factor 3*k - 2*k - 4 + 30*k**2 + y*k - 3*k.
2*(3*k + 1)*(5*k - 2)
Let q(c) = c - 7. Let s be q(14). Suppose s*d**4 - 29/4*d**3 - 1/4*d**2 + 0 + 1/2*d = 0. What is d?
-1/4, 0, 2/7, 1
Let h(d) be the third derivative of d**6/120 + d**5/15 + d**4/8 + 36*d**2. Solve h(w) = 0 for w.
-3, -1, 0
Let g = -21 - -21. Let a(i) be the first derivative of 1/4*i**4 + 0*i + 1 + g*i**2 - 1/9*i**3. Determine v, given that a(v) = 0.
0, 1/3
Suppose 2/3*z**3 - 8/3*z**5 + 1/3 + 11/3*z**2 - 4*z**4 + 2*z = 0. Calculate z.
-1, -1/2, 1
Let a(q) be the first derivative of q**8/840 + q**7/210 - q**5/30 - q**4/12 + q**3/3 - 1. Let f(p) be the third derivative of a(p). Factor f(h).
2*(h - 1)*(h + 1)**3
Suppose -13 = -m - 3. Determine o, given that 5*o**2 - 14*o + 2*o**3 - 3*o**2 + m*o = 0.
-2, 0, 1
Let j = 3 - 1. Factor -6*s**3 - 5*s**2 - j*s**3 - s**3 - 3*s**4 - 4*s**2 - 3*s.
-3*s*(s + 1)**3
Let u(s) be the third derivative of s**8/20160 - s**7/5040 + s**5/30 + 4*s**2. Let i(d) be the third derivative of u(d). Solve i(j) = 0 for j.
0, 1
Factor -8/3*n + 0 - 4/3*n**2.
-4*n*(n + 2)/3
Let q = -22/3 - -23/3. Let 5/6*k**4 - 1/2*k**2 - 7/6*k - q + 7/6*k**3 = 0. Calculate k.
-1, -2/5, 1
What is j in -6/7*j - 2/7*j**2 - 4/7 = 0?
-2, -1
Let k(q) be the second derivative of q**5/15 - 7*q**4/18 - 5*q**3/9 + 4*q**2/3 - 21*q. Suppose k(v) = 0. What is v?
-1, 1/2, 4
Let b be ((-2)/4 - 33/(-6)) + 0. Suppose -3*f**b - 3/4*f**3 + 0 - 15/4*f**4 + 0*f + 0*f**2 = 0. What is f?
-1, -1/4, 0
Suppose 16 = 24*k - 80. Determine j so that 2/3*j**5 - 2/9 + 14/9*j - 26/9*j**4 - k*j**2 + 44/9*j**3 = 0.
1/3, 1
Let o(b) be the third derivative of 1/12*b**3 + 1/120*b**5 + 1/24*b**4 - 3*b**2 + 0*b + 0. Factor o(z).
(z + 1)**2/2
Let w(r) be the third derivative of 1/84*r**4 + 0*r - 1/420*r**6 - 7*r**2 + 0 + 0*r**3 + 0*r**5. Solve w(x) = 0.
-1, 0, 1
Let w(f) be the third derivative of -f**5/15 - f**4 + f**2. Solve w(u) = 0 for u.
-6, 0
Let y be 2/25*(22 - 17). Factor y*x**2 + 4/5 + 6/5*x.
2*(x + 1)*(x + 2)/5
Suppose -m + 2 = -0. Let h be m + -1 + (-4)/(-4). Determine l, given that -4/3*l**2 - 2*l + 2/3*l**5 + 4/3*l**3 + h*l**4 - 2/3 = 0.
-1, 1
Factor 9*u + 14*u - 11*u + 3*u**2 + u**2.
4*u*(u + 3)
Let s be (-2 - -2) + 2 + 1. Suppose -s*i + 5*f + 23 = -i, 23 = 5*i - f. Factor 9*h**2 + 2*h**i - 4*h**3 - h**2 - 6*h**2.
2*h**2*(h - 1)**2
Let g(b) be the first derivative of -2*b**3/3 - 4*b**2 - 6*b + 17. Factor g(j).
-2*(j + 1)*(j + 3)
Suppose 0 = 2*s + 3*s. Suppose s = -3*f + 6*f - 9. What is g in -15*g**2 + 9/2*g**3 - f + 27/2*g = 0?
1/3, 1, 2
Let f(o) be the second derivative of -o**5/60 + o**4/18 - o**3/18 - 7*o. Factor f(u).
-u*(u - 1)**2/3
Suppose 2*m = 5*m - 9. Let x(z) be the first derivative of 1 - 1/3*z**m - z - z**2. Factor x(d).
-(d + 1)**2
Factor -2 - 12*w - 3*w + 14 + 3*w**2.
3*(w - 4)*(w - 1)
Suppose 8*u = 8 + 8. Let z(b) be the first derivative of -3/5*b**u - 1/10*b**4 - 2/5*b - 2/5*b**3 - 1. Let z(k) = 0. Calculate k.
-1
What is z in -28/5*z**2 - 4/5*z**3 + 4*z + 60 = 0?
-5, 3
Let v(o) be the first derivative of -1/90*o**6 - 1/6*o**2 - 3 + 3*o + 1/18*o**4 + 0*o**3 + 0*o**5. Let g(p) be the first derivative of v(p). Factor g(z).
-(z - 1)**2*(z + 1)**2/3
Let t(i) = 5*i**4 - 16*i**3 + 5*i**2 - 6*i. Let l(w) = 70*w**4 - 225*w**3 + 70*w**2 - 85*w. Let c(s) = -6*l(s) + 85*t(s). Let c(k) = 0. What is k?
0, 1
Let f = 26862 - 187398/7. Let a = -90 + f. Solve -a*v**3 + 6/7*v - 2/7*v**2 - 2/7*v**4 + 4/7 = 0.
-2, -1, 1
Let w(c) be the first derivative of -c**2 - 4*c - 2. Let k be w(-3). Factor -8/7 + 8/7*a - 2/7*a**k.
-2*(a - 2)**2/7
Let i(h) be the first derivative of 0*h - 2 + 1/3*h**3 - h**2 + 0*h**4 - 1/30*h**5. Let m(a) be the second derivative of i(a). Suppose m(f) = 0. What is f?
-1, 1
Let s(k) be the first derivative of -49*k**5/160 - 7*k**4/3 - 29*k**3/12 - k**2 - k + 10. Let n(d) be the first derivative of s(d). Let n(a) = 0. What is a?
-4, -2/7
Let r(b) be the first derivative of 4*b**5/9 - 37*b**4/36 - 8*b**3/27 + 2*b**2/9 - 7. What is i in r(i) = 0?
-2/5, 0, 1/4, 2
Let j(o) be the first derivative of o**6/2 - 6*o**5/5 - 9*o**4/4 + 4*o**3 + 6*o**2 + 8. Factor j(u).
3*u*(u - 2)**2*(u + 1)**2
Let f be 14/7 + 0/2. Factor f*u**3 + 2*u**5 + 13*u**4 - 6*u**4 - 6*u**2 - 4*u - u**4.
2*u*(u - 1)*(u + 1)**2*(u + 2)
Let u be (68/(-24) - 1) + 4. Let g(k) be the second derivative of 0 + 0*k**2 - u*k**4 + 0*k**3 + 2*k. Factor g(h).
-2*h**2
Let r(o) be the second derivative of 1/3*o**2 + 1/18*o**4 + 0 + 2/9*o**3 - 2*o. Factor r(d).
2*(d + 1)**2/3
Let a(s) be the second derivative of -1/24*s**3 + 0 - 1/48*s**4 + 1/4*s**2 - 4*s. Factor a(t).
-(t - 1)*(t + 2)/4
Determine n so that -5*n**2 + n**3 + 3*n**2 + 3*n - 5*n + 3*n**2 = 0.
-2, 0, 1
Solve 0*x**2 - 2/3*x**3 + 2*x - 4/3 = 0.
-2, 1
Factor 4/3*c**5 - 4/3*c**4 + 8/3*c**2 + 4/3*c - 8/3*c**3 - 4/3.
4*(c - 1)**3*(c + 1)**2/3
Factor -12/7*x**2 - 16/7 + 2/7*x**3 + 24/7*x.
2*(x - 2)**3/7
Let y(d) be the second derivative of d**7/21 - d**6/5 - 2*d**5/5 + 2*d - 9. Let y(m) = 0. What is m?
-1, 0, 4
Suppose -48*d + 8*d**2 + 33*d - 3*d**2 = 0. Calculate d.
0, 3
What is b in 6 - 26 + b**2 - 6*b**2 - 20*b = 0?
-2
Let y(w) = w**2 + 5*w + 4. Let j be y(-4). Let v = j - -3. Factor 0*t + 2*t**v - 3*t**3 + 0*t.
-t**3
Let y(t) be the second derivative of t**5/30 + t**4/18 - 5*t**3/9 + t**2 + 8*t. Suppose y(i) = 0. What is i?
-3, 1
Let k(d) = -6*d**5 + 3*d**4 + 3*d**3 - 3*d**2 + 3*d. Let l(z) = -z**5 + z. Let f(h) = -k(h) + 3*l(h). Determine r, given that f(r) = 0.
-1, 0, 1
Let x(b) be the first derivative of -b**3/15 - 4. Factor x(n).
-n**2/5
Let w(h) be the third derivative of 0*h**4 - 7/60*h**6 + 0*h**3 + 3*h**2 + 0 - 1/15*h**5 + 0*h. Suppose w(a) = 0. What is a?
-2/7, 0
Suppose 1/4*n**2 - 3/2*n + 9/4 = 0. What is n?
3
Let u(p) = p + 4. Let j be u(-1). Let r(z) be the second derivative of 3*z - 1/8*z**j + 0 + 1/4*z**2 + 1/48*z**4. Factor r(y).
(y - 2)*(y - 1)/4
Let x = -9 + 12. Determine d so that 3*d - 3*d**3 + d**2 - d**4 + 0*d**x - 2*d**4 + 2*d**2 = 0.
-1, 0, 1
Suppose 27 = -5*y + 14*y. Find a, given that a**y - a + 2/7*a**2 - 2/7 = 0.
-1, -2/7, 1
Let r(y) = -y**2 - 5*y - 2. Let m be r(-5). Let q = 0 - m. Factor -1 + 2*k**2 + k**q - 2*k**2.
(k - 1)*(k + 1)
Let w(i) = 6*i**5 - 6*i**4 - 9*i**3 + 6*i**2 + 9*i - 6. Let k(m) = -m**5 + 2*m**4 - m**3. Let u(d) = 3*k(d) + w(d). Suppose u(c) = 0. What is c?
-2, -1, 1
Let g(v) = 2*v**2 - 3*v + 1. Let o be g(2). Factor 3*c**2 + o - 3 - 3.
3*(c - 1)*(c + 1)
Let u(y) be the third derivative of -y**6/900 - y**5/300 - y**3/2 - 2*y**2. Let t(l) be the first derivative of u(l). Factor t(b).
-2*b*(b + 1)/5
Let i(z) = 17*z**2 + 17*z - 13. Let k(n) = -8*n**2 - 8*n + 6. Let r(j) = 6*i(j) + 13*k(j). Suppose r(v) = 0. Calculate v.
-1, 0
Let q(o) be the third derivative of -1/36*o**4 + 1/180*o**6 + 0*o**5 + 0 - 6*o**2 + 0*o + 0*o**3. Suppose q(l) = 0