f -i**6/180 - i**5/45 + i**4/36 + 2*i**3/9 + 5*i**2. What is f in a(f) = 0?
-2, -1, 1
Let f(u) be the first derivative of u**6/3 - 2*u**5/5 - u**4/2 + 2*u**3/3 + 33. Factor f(v).
2*v**2*(v - 1)**2*(v + 1)
Let y(q) = 12*q**2 + 47*q + 11. Let h(m) = 4*m**2 + 16*m + 4. Suppose 3*f - 2 = 31. Let o(t) = f*h(t) - 4*y(t). Factor o(p).
-4*p*(p + 3)
Let b(r) be the second derivative of r**7/105 - r**5/30 - r**2 - 4*r. Let h(o) be the first derivative of b(o). Factor h(z).
2*z**2*(z - 1)*(z + 1)
Find o such that 6*o**2 + 24*o**2 - 6*o - 4 - 2*o**2 = 0.
-2/7, 1/2
Let k be (3 - 7)/((-2)/4). Factor 18*w**2 + 8*w + 2 - 3*w + 9*w + k*w**3 - 2*w.
2*(w + 1)**2*(4*w + 1)
Suppose -f + 6 = 3*y + 3*f, -2*f - 6 = -3*y. Factor 0*i**2 - i**2 + 3*i**3 + y*i**2 + 2*i**2.
3*i**2*(i + 1)
Let v(h) be the first derivative of -h**5/10 - h**4/8 + h**3/2 + h**2/4 - h + 27. Factor v(z).
-(z - 1)**2*(z + 1)*(z + 2)/2
Let t(x) be the first derivative of x**4/20 + x**3/5 - 3. Determine s, given that t(s) = 0.
-3, 0
Let q(m) be the first derivative of -m**3/18 + 8*m/3 - 48. Factor q(u).
-(u - 4)*(u + 4)/6
Let n(c) be the second derivative of -1/40*c**5 + c**2 - 5*c + 0*c**3 + 0 - 1/8*c**4. Find y, given that n(y) = 0.
-2, 1
Suppose 4*i - 10 = -i. Let -4*p - 10*p + 12 + 3*p**2 + 0*p + i*p = 0. What is p?
2
Let s(c) be the third derivative of c**9/25200 + 3*c**8/11200 + c**7/1400 + c**6/1200 + c**4/8 + 2*c**2. Let o(u) be the second derivative of s(u). Factor o(f).
3*f*(f + 1)**3/5
Factor -4*j**3 - 2*j + 6*j**3 + 2*j**2 - 2 + 0*j.
2*(j - 1)*(j + 1)**2
Let i be ((-2)/(-3))/(15/9). Let p(f) = 13*f - 88. Let c be p(7). Factor -2/5*j + 2/5 + i*j**c - 2/5*j**2.
2*(j - 1)**2*(j + 1)/5
Let v(y) be the first derivative of -y**5/60 + y**4/24 + 2*y**2 + 4. Let b(a) be the second derivative of v(a). Factor b(w).
-w*(w - 1)
Let m(z) be the first derivative of -z**3/3 + z**2 - z + 24. Find x such that m(x) = 0.
1
Let i(a) = -6*a**2 - 7*a. Let n be (2/4)/((-4)/56). Let p(j) = -5*j**2 - 6*j. Let r(h) = n*p(h) + 6*i(h). Factor r(b).
-b**2
Let w(d) be the first derivative of -3/25*d**5 - 3/5*d**3 + 0*d - 3/10*d**2 + 2 - 9/20*d**4. Suppose w(o) = 0. Calculate o.
-1, 0
Let u(q) be the second derivative of q**5/90 + q**4/36 - q**2 + 7*q. Let f(p) be the first derivative of u(p). Factor f(y).
2*y*(y + 1)/3
Suppose -2/3*m**2 - 4/3*m**3 + 2/3*m**4 + 0 + 4/3*m = 0. Calculate m.
-1, 0, 1, 2
Suppose q + 2 + 0 = 2*m, -3*q - 5*m + 16 = 0. Suppose -2*z**3 - z**3 + 2*z + q*z**3 - 3*z**2 - 4*z**3 = 0. Calculate z.
-1, 0, 2/5
Suppose -2*z - 18 = -4*g, 2*z - 3 = g - 15. Suppose 5*l = -3 - g. Let t(n) = -n - 1. Let x(w) = 2*w**2 - 5*w - 7. Let h(f) = l*x(f) + 3*t(f). Solve h(y) = 0.
-1, 2
Let c(i) be the second derivative of -i**4/3 + 16*i**3/3 - 32*i**2 - 7*i. Find q such that c(q) = 0.
4
Let l = -19 + 16. Let n be 8/(-12)*l/5. Factor 2/5*g**5 + 0 - n*g**3 + 0*g + 0*g**2 + 0*g**4.
2*g**3*(g - 1)*(g + 1)/5
Let k = -3 - -4. Let n be (2/1)/k - 0. Factor 0*l + l + l - n*l**3.
-2*l*(l - 1)*(l + 1)
Suppose 2/9*j**2 + 0 + 1/9*j + 1/9*j**3 = 0. What is j?
-1, 0
Let r = -24 - -26. Factor -1/3*w**r - 2/3 + w.
-(w - 2)*(w - 1)/3
Let k = -4 + 7. Suppose k*p + 3*g = 3, -5*p = 2*g - 5*g - 21. Determine b, given that 4*b**4 + b**5 + 2*b + 4*b**2 + 0*b**3 - b - b**p + 7*b**3 = 0.
-1, 0
Let h be (-1 - -2)/(-1) - -5. Let k(l) be the third derivative of 0*l + 1/60*l**5 - l**2 - 1/8*l**h + 1/3*l**3 + 0. Factor k(x).
(x - 2)*(x - 1)
Let i(z) = -z**2 - z - 1. Let v(m) = 16*m**2 + 18*m + 16. Let l(s) = 28*i(s) + 2*v(s). Let l(o) = 0. What is o?
-1
Let o be (2/(-15)*-40)/(5/3). Factor 6/5*z**2 + 8/5 - o*z.
2*(z - 2)*(3*z - 2)/5
Let u(d) be the first derivative of 9*d**5/50 + d**4/10 - d**3/3 + d**2/5 + 4*d + 5. Let v(m) be the first derivative of u(m). Solve v(z) = 0 for z.
-1, 1/3
Suppose 0 = -2*t - 1 + 5. Solve -2*x**2 + t*x + 0*x**2 - 4 + 2*x + 2*x = 0.
1, 2
Let n(f) be the second derivative of -2*f + 0*f**3 + 0 + 0*f**2 - 3/20*f**5 - 1/2*f**4. Let n(o) = 0. Calculate o.
-2, 0
Suppose d - 3*v - 42 = -4*d, 0 = 5*d + v - 26. Let x = d + -4. Determine l, given that -2/3*l**x - 2*l - 4/3 = 0.
-2, -1
Let f(g) = -9*g**2 - 3*g + 12. Let v be f(8). Let s = -1744/3 - v. Find y, given that s*y**2 + 8/3*y**3 + 10/3*y**5 - 6*y - 8*y**4 + 4/3 = 0.
-1, 2/5, 1
Let w be (-16)/(-6)*(-6)/(-24). Factor -2/3*g + 0 + w*g**2 - 2/3*g**4 + 2/3*g**3.
-2*g*(g - 1)**2*(g + 1)/3
Suppose -5*q + 7*j = 4*j + 12, 3*q = -3*j + 12. What is d in q + 1/3*d**2 - 1/3*d = 0?
0, 1
Let m(g) be the second derivative of g**5/190 + 5*g**4/114 + 7*g**3/57 + 3*g**2/19 - 7*g. Suppose m(h) = 0. Calculate h.
-3, -1
Let o(a) be the third derivative of 0 - 1/6*a**3 + 0*a + 1/60*a**5 + 0*a**4 + a**2. Factor o(b).
(b - 1)*(b + 1)
Suppose 2*l + 3*l + 4*a = 444, -4*l = -4*a - 384. Let r = l - 179/2. Factor -r*u**2 + 0 + 3/2*u**3 + 1/2*u + 9/2*u**4.
u*(u + 1)*(3*u - 1)**2/2
Let q = 27 - 25. Let z(l) be the first derivative of -1/9*l**3 + 1/18*l**6 + 0*l**q + 2 + 0*l + 1/4*l**4 - 1/5*l**5. Factor z(d).
d**2*(d - 1)**3/3
Let x = -1036 + 7222/7. Let r = 169/28 + x. Let 1/2 - r*m**2 - 5/4*m = 0. Calculate m.
-1, 2/7
Let 2/13 - 6/13*u + 6/13*u**2 - 2/13*u**3 = 0. Calculate u.
1
Factor -11*b**2 - 5*b**3 + 16*b**2 - 4*b**2 - 6*b**2.
-5*b**2*(b + 1)
Let b = -21 + 3. Let v be (-8 - -2)*b/24. Factor -15/2*w + v*w**2 + 3.
3*(w - 1)*(3*w - 2)/2
Let m(o) be the first derivative of 3*o**5/70 - o**4/42 - 8*o**3/21 - 4*o**2/7 + o + 1. Let c(r) be the first derivative of m(r). Factor c(g).
2*(g - 2)*(g + 1)*(3*g + 2)/7
Factor -s**2 + s**3 - 4 + 3*s**2 + s**2.
(s - 1)*(s + 2)**2
Factor -1/5*s**2 + 0 + 1/5*s**4 + 1/5*s - 1/5*s**3.
s*(s - 1)**2*(s + 1)/5
Let g be (1/2)/(4/24). Let x be (1/(-3))/((-3)/6). Factor -2/3*q**4 - 4/3*q + 0*q**2 + x + 4/3*q**g.
-2*(q - 1)**3*(q + 1)/3
Factor 0*b**3 + 6*b**2 - 6*b**3 - 3*b**4 - 4 + 1 + 3*b**5 + 3*b.
3*(b - 1)**3*(b + 1)**2
Suppose -39 = -6*d + 15. Determine n, given that -57/4*n**4 - d*n**5 - n**3 + 9/2*n**2 - 1/4 + 0*n = 0.
-1, -1/4, 1/3
Let p = 4/5 + -7/15. Let b(i) be the first derivative of 2 + i + p*i**3 + i**2. Let b(h) = 0. What is h?
-1
Factor -12 + 6*w**2 - 10*w**2 - 23*w**2 - 36*w.
-3*(3*w + 2)**2
Suppose -2*t = -5*x + 22, 6*x = x - 3*t + 17. Factor 32*y**4 + 8*y**3 - 8*y**4 + 10*y**5 + 10*y**3 + x*y**2.
2*y**2*(y + 1)**2*(5*y + 2)
Let z(l) be the first derivative of l**8/4200 - l**6/300 - l**5/150 + l**3/3 - 1. Let v(f) be the third derivative of z(f). Determine c, given that v(c) = 0.
-1, 0, 2
Let a(y) be the first derivative of 7/10*y**2 - 2/5*y - 5 - 1/3*y**3. Factor a(f).
-(f - 1)*(5*f - 2)/5
Let x(w) be the second derivative of -w**5/26 + w**4/39 - 14*w. Factor x(a).
-2*a**2*(5*a - 2)/13
Let j(s) = -17*s**2 + 3*s + 27. Let k(z) = -8*z**2 + 2*z + 13. Let y(b) = -3*j(b) + 7*k(b). What is c in y(c) = 0?
-1, 2
Let u = -16 - -16. Let a be u/((-1 - -2)*-1). Factor 0*n**2 + 0*n**4 + a*n + 0 + 2/5*n**3 - 2/5*n**5.
-2*n**3*(n - 1)*(n + 1)/5
Let a(r) = r**2 + 2*r - 1. Let z = 6 + -5. Let h be a(z). What is g in 6*g**2 + h + g**3 + 3*g**3 + 6*g + 0*g**3 - 2*g**3 = 0?
-1
Let w(x) be the third derivative of -x**5/210 - x**4/42 - x**3/21 + x**2. Factor w(a).
-2*(a + 1)**2/7
Let f = 234 + -232. Determine g, given that -8/11 - 2/11*g**f + 8/11*g = 0.
2
Suppose -l + 4*b - 17 = 0, -7*l = -2*l - 3*b. Solve 0*o - l - 2*o**2 + 1 - 4*o = 0 for o.
-1
Let r(p) = 0*p + p - 5*p**2 + 4*p**2 + 0*p**2. Let g = -3 + 2. Let d(a) = -a**4 - 2*a**3 + 4*a**2 - 5*a. Let w(c) = g*d(c) - 5*r(c). Solve w(v) = 0.
-1, 0
Let g be 7*20/175 - 2/10. Solve 0*c + 0 + g*c**4 + 3/5*c**2 + 6/5*c**3 = 0 for c.
-1, 0
Suppose 0 = -5*b + b + 12. Find y such that -y**2 - 2*y**2 + b + 3*y**3 - 3 - 6*y = 0.
-1, 0, 2
Let a(j) be the first derivative of -1/2*j**5 - 2/3*j**3 - j - 2 + 0*j**2 + 7/6*j**4. Let u(l) be the first derivative of a(l). Find f such that u(f) = 0.
0, 2/5, 1
Let d(s) be the first derivative of -s**4/16 - s**3/2 - 3*s**2/2 - 2*s + 19. Factor d(a).
-(a + 2)**3/4
Let v(z) be the second derivative of -z**5/80 - z**4/24 - z**3/24 - 7*z. Find c, given that v(c) = 0.
-1, 0
Let m(p) be the third derivative of 4*p**2 + 1/12*p**3 + 1/240*p**6 + 1/40*p**5 + 1/16*p**4 + 0*p + 0. Factor m(d).
(d + 1)**3/2
Let a = -2 + 9. Factor -8*c**2 + 2*c**2 + a*c**3 - 1 - c + 5*c - c**4 - 3*c**3.
-(c - 1)**4
L