Find a such that 8*a**4 + 3*a**3 + 4*a**4 + 4*a**4 - 3*a**5 + 3*a**2 - 19*a**4 = 0.
-1, 0, 1
Let a(s) be the second derivative of -s**6/165 + 2*s**5/55 - s**4/33 - 4*s**3/33 + 3*s**2/11 + 7*s. Suppose a(d) = 0. Calculate d.
-1, 1, 3
Let l(c) be the first derivative of -3*c**4/4 + 2*c**3 + 9*c**2/2 + 7. Factor l(n).
-3*n*(n - 3)*(n + 1)
Let w(n) be the second derivative of -125*n**7/147 + 5*n**6/21 + 19*n**5/7 + 3*n**4/7 - 27*n**3/7 - 27*n**2/7 - 3*n. Factor w(m).
-2*(m - 1)**2*(5*m + 3)**3/7
Factor 0 - v**4 - 3/2*v**3 - 1/2*v**2 + 0*v.
-v**2*(v + 1)*(2*v + 1)/2
Solve 2/13*i - 2/13*i**4 - 2/13 + 2/13*i**5 - 4/13*i**3 + 4/13*i**2 = 0 for i.
-1, 1
Factor 4*b**3 + 8*b + 0*b**3 - 18*b**2 + 64 - 64.
2*b*(b - 4)*(2*b - 1)
Let a(o) be the second derivative of o**4/21 - 2*o**2/7 + 16*o. Factor a(i).
4*(i - 1)*(i + 1)/7
Let v(u) be the third derivative of -u**6/30 + u**5/3 - u**4/3 - 16*u**3/3 - 11*u**2 - u. Determine a so that v(a) = 0.
-1, 2, 4
Let r(a) = -2*a**2 - 7*a + 5. Let y(i) = 0 - 2 + i - 2 + 3. Let w(f) = r(f) + 5*y(f). Suppose w(p) = 0. Calculate p.
-1, 0
Let q(b) be the second derivative of -7*b**3 + 0 + 3*b - 49/8*b**4 - 3*b**2. Factor q(i).
-3*(7*i + 2)**2/2
Let k be (-3*(-1 + 0))/1. Let j = k + 0. Solve -g**2 + 7*g**j + 5*g**2 - 2*g**2 = 0.
-2/7, 0
Let j(p) be the first derivative of -9*p**4/4 - 16*p**3/3 + 2*p**2 - 47. Determine g so that j(g) = 0.
-2, 0, 2/9
Let i = 53 + -53. Determine j so that 1/2*j**2 + i - 1/2*j = 0.
0, 1
Suppose -o = 3*o. Let g(i) be the first derivative of -14/5*i**5 + 0*i**2 - i**6 - 5/2*i**4 - 2/3*i**3 - 1 + o*i. Factor g(q).
-2*q**2*(q + 1)**2*(3*q + 1)
Suppose -5*x = -3*x. Let z(d) be the third derivative of x*d + 1/48*d**4 - 1/240*d**5 + 2*d**2 + 0*d**3 + 0. Find g such that z(g) = 0.
0, 2
Let o be 3/7 - (-16)/28. Let s(i) be the first derivative of -4/3*i**2 - 2/9*i**3 - o - 8/3*i. Factor s(z).
-2*(z + 2)**2/3
Let a(x) be the second derivative of -2*x**7/63 + 2*x**6/9 - 8*x**5/15 + 4*x**4/9 - 20*x. Factor a(r).
-4*r**2*(r - 2)**2*(r - 1)/3
Let p(r) be the first derivative of r**4/2 + 4*r**3/3 - r**2 - 4*r + 2. Solve p(k) = 0.
-2, -1, 1
Let r(q) be the third derivative of q**8/168 + q**7/105 - q**6/12 - q**5/30 + 2*q**4/3 - 4*q**3/3 + 3*q**2. Factor r(m).
2*(m - 1)**3*(m + 2)**2
Suppose 0 = -2*m - f - 55, 35 = -m + 2*f - 5. Let b be (m/(-25))/(14/30). Factor 6/7*o**3 - b*o**4 + 10/7*o**2 + 2/7*o + 0.
-2*o*(o - 1)*(3*o + 1)**2/7
Factor 40/3*a**2 + 26/3*a + 4/3 + 6*a**3.
2*(a + 1)**2*(9*a + 2)/3
Let k(p) = -p**2 - 2*p + 2. Let m(q) = -4*q**2 - 6*q + 7. Let g(l) = 5*l + 3. Let r be g(-2). Let z(a) = r*k(a) + 2*m(a). Suppose z(v) = 0. What is v?
0, 2
Let j = 2 + 0. Suppose -7 - 2*u + 0*u**2 + 3 - 4*u**2 + 6*u**j = 0. Calculate u.
-1, 2
Let f = -1014/55 + 216/11. Factor f*v**2 - 2/5 - 4/5*v**3 + 0*v.
-2*(v - 1)**2*(2*v + 1)/5
Let p = 17 + -17. Let v(h) be the second derivative of -7/12*h**4 + p*h**2 + 1/6*h**3 + h + 3/4*h**5 - 3/10*h**6 + 0. Factor v(b).
-b*(b - 1)*(3*b - 1)**2
Factor -2/7*g**3 - 2/7*g**2 + 2/7 + 2/7*g.
-2*(g - 1)*(g + 1)**2/7
Let v(a) be the second derivative of 1/5*a**3 + 0 - 3/10*a**2 - 2*a - 1/20*a**4. Suppose v(o) = 0. What is o?
1
Factor -2/9*j - 2/9*j**2 + 0.
-2*j*(j + 1)/9
Suppose -2*d = 3*d - 40. Factor d - 1 - 3*s - 1 - 3*s**2.
-3*(s - 1)*(s + 2)
Let c(u) be the first derivative of 2*u**3/3 + u**2 + 8. Factor c(k).
2*k*(k + 1)
What is l in 0 - 2/3*l + 7*l**2 = 0?
0, 2/21
Let y(g) = 1 - 2 - 7*g**2 - 1 - 3*g. Let l(o) = -6*o**2 - 2*o - 2. Let a(s) = 6*l(s) - 5*y(s). Find j such that a(j) = 0.
1, 2
Factor 1/2*y**5 + 1/2 + 1/2*y**4 + 1/2*y - y**2 - y**3.
(y - 1)**2*(y + 1)**3/2
Let r(l) be the second derivative of l**7/2520 - l**6/1080 - l**5/360 + l**4/72 + l**3/2 - 3*l. Let d(g) be the second derivative of r(g). Factor d(z).
(z - 1)**2*(z + 1)/3
Let j = 34 + -32. Let m(i) be the second derivative of 0*i**6 + 0 + 1/60*i**5 + 0*i**4 - 3*i + 0*i**3 - 1/126*i**7 + 0*i**j. Factor m(g).
-g**3*(g - 1)*(g + 1)/3
Let b(x) be the third derivative of -x**7/70 + 7*x**6/40 - 2*x**5/5 - 2*x**4 - 2*x**2. Factor b(d).
-3*d*(d - 4)**2*(d + 1)
Suppose 0 = 3*w + 12*w - 30. Let h(a) be the second derivative of 3*a + 0 - 1/5*a**3 - 1/50*a**5 - 1/10*a**4 - 1/5*a**w. Find z such that h(z) = 0.
-1
Let b(j) = -j**2 + 6*j - 6. Let z be b(4). Let u = -1 + z. Determine c, given that 2 + c**3 - 2 + u - c**2 - c = 0.
-1, 1
Let t(u) = -2*u**2 - 2*u + 2. Let d(b) = 1. Let z(o) = -4*d(o) - 2*t(o). Factor z(m).
4*(m - 1)*(m + 2)
Let j be (6/5)/((-30)/(-100)). Let o(v) be the third derivative of 1/360*v**6 + v**2 + 1/24*v**j + 0 + 1/60*v**5 + 1/18*v**3 + 0*v. Solve o(g) = 0 for g.
-1
Let u(c) be the third derivative of -c**6/1080 + c**4/216 - 13*c**2. Solve u(f) = 0.
-1, 0, 1
Suppose 0*n**2 + 2*n**2 + 10*n + 13*n - 13*n = 0. What is n?
-5, 0
Suppose -2*n = -2 - 0. Let q = 3 - n. Suppose 2 + 0*t**2 - 4*t - 3*t**q + 5*t**2 = 0. Calculate t.
1
Let q(n) = n**3 - 1. Let s(y) = 8*y**3 + 30*y**2 + 45*y - 3. Let v(g) = 3*q(g) - s(g). Solve v(f) = 0.
-3, 0
Suppose -20 = 5*b + 4*d, 5 = -2*d - 5. Let r(s) be the third derivative of b + 1/120*s**5 + 0*s**3 + 1/24*s**4 + 0*s - 4*s**2. Factor r(l).
l*(l + 2)/2
Let k = -10 - -13. Suppose k*q - 3*q**3 - 14*q**4 + q**2 + 11*q**4 + 2*q**2 = 0. Calculate q.
-1, 0, 1
Let r(y) be the second derivative of -49*y**6/15 - 112*y**5/5 - 52*y**4 - 128*y**3/3 - 16*y**2 + 5*y. Factor r(g).
-2*(g + 2)**2*(7*g + 2)**2
Factor 0 + 1/4*w**2 + 0*w.
w**2/4
Let f(q) = -q + 6. Let j be f(-6). Let b be 2/(-2) + 16/j. Let -u**3 - 2/3 + u + 1/3*u**2 + b*u**4 = 0. What is u?
-1, 1, 2
Let i = 8 + -6. Let a(p) be the second derivative of 31/48*p**4 + 1/2*p**i + 2*p + 5/6*p**3 + 0 + 3/16*p**5. What is x in a(x) = 0?
-1, -2/3, -2/5
Factor 4*x**3 - 2*x**4 - 4*x**2 + 3*x**4 + x**4 - 2*x**3.
2*x**2*(x - 1)*(x + 2)
Factor -49*o**2 - 136*o + 45 - 74*o + 294*o**2.
5*(7*o - 3)**2
Let g(r) be the first derivative of -1/900*r**6 - 1/3*r**3 + 0*r**2 - 1/15*r**4 + 0*r + 1/75*r**5 + 2. Let q(z) be the third derivative of g(z). Solve q(o) = 0.
2
Suppose -3*l - 8 = 2*p + l, 2*p + l = 1. Suppose -w + 0*w + p = 0. Factor -d - 4*d**2 - 2 - 3*d + w*d**2.
-2*(d + 1)**2
Let l(y) be the third derivative of -1/4*y**4 - 1/20*y**5 + 0*y + 1/40*y**6 + 5*y**2 + 0*y**3 + 0. Solve l(m) = 0 for m.
-1, 0, 2
Factor 6/5 + r + 1/5*r**2.
(r + 2)*(r + 3)/5
Let m be 2/19 + 182/798. Factor -m*c**3 + 0 - 2/3*c**2 - 1/3*c.
-c*(c + 1)**2/3
Let v(j) be the third derivative of -5*j**8/336 - j**7/7 - 3*j**6/8 - 29*j**2. Let v(x) = 0. What is x?
-3, 0
Let u(r) = r - 2. Let s be u(6). Factor s*g**3 - 10*g**4 + 14*g**5 - 8*g**3 + 0*g**3.
2*g**3*(g - 1)*(7*g + 2)
Suppose 4*o - 8*o + 12 = 0. Suppose -o*h = h. Suppose 0*g + 0*g**3 + 1/3*g**4 - 1/3*g**2 + h = 0. What is g?
-1, 0, 1
Suppose 2*d = -u + 29, -2*d = -4*d + u + 19. Suppose -3*s - s + d = 2*o, 3*o = -5*s + 16. What is z in -12*z**s + 3*z + z - z + 0*z = 0?
0, 1/4
Let x(l) be the first derivative of -32*l**5/15 - 16*l**4/3 + 98*l**3/9 + 2*l**2/3 - 2*l - 13. Suppose x(y) = 0. Calculate y.
-3, -1/4, 1/4, 1
Let w = 3/95 + 887/1995. Let y(i) be the third derivative of 27/140*i**6 - 39/70*i**5 + w*i**4 - 4/21*i**3 + 0 + 2*i**2 + 0*i. Factor y(u).
2*(u - 1)*(9*u - 2)**2/7
Let k be 0 + (-1 - (3 + -4)). Factor w**3 + k*w**3 + w**2 + 0*w**3.
w**2*(w + 1)
Let o(d) = 2*d - 6. Let c be o(5). Determine z so that 35*z**4 - 8*z - 39*z**c + 5*z**3 + 3*z**3 + 4*z**2 = 0.
-1, 0, 1, 2
Let b = 190/33 - 56/11. Factor 4/3 + 0*u**2 - 2*u + b*u**3.
2*(u - 1)**2*(u + 2)/3
Let v(i) = -i**2 - i + 1. Let o be v(0). Find f such that 1/4*f**2 + o - f = 0.
2
Let i(o) = 2*o**4 + 7*o**3 + 15*o**2 + 11*o + 7. Let t(x) = -10*x**4 - 36*x**3 - 76*x**2 - 56*x - 34. Let s(p) = 28*i(p) + 6*t(p). Determine k so that s(k) = 0.
-2, -1
Let r(v) be the second derivative of -5/2*v**3 + 3/4*v**4 + 3*v**2 + 0 + v. Find j such that r(j) = 0.
2/3, 1
Let i(d) be the third derivative of d**6/120 + 3*d**5/40 + d**4/4 - d**3/2 - 6*d**2. Let g(r) be the first derivative of i(r). Factor g(m).
3*(m + 1)*(m + 2)
Suppose 1/5 - 2/5*p + 1/5*p**2 = 0. Calculate p.
1
Factor -3*x**3 - 219*x**2 - 60 - 216*x**2 + 408*x**2 - 72*x.
-3*(x + 2)**2*(x + 5)
Let r = 183 + -183. Find h, given that r*h**4 - 3/2*h + 3*h**3 + 0*h**2 - 3/2*h**5 + 0 = 0.
-1, 0, 1
Let u(h) = 11*h**2