e of k**10/151200 - k**9/75600 + k**4/12 + 3*k**2. Let c(i) be the second derivative of r(i). Find v such that c(v) = 0.
0, 1
Suppose 20*w**4 + 4*w**2 + 2*w + 56*w**3 - 2*w - 8*w**5 - 72*w**3 = 0. Calculate w.
0, 1/2, 1
Suppose -3*k - 3*i = i + 16, -2*i - 8 = -5*k. Determine x so that 9*x + 2*x**2 + k + 5 - 15*x - 1 = 0.
1, 2
Suppose 0 = 5*s + 2*s - 14. Factor -56/9*z + 8/9 + 98/9*z**s.
2*(7*z - 2)**2/9
Let i(b) be the third derivative of -b**6/420 + b**5/35 - 3*b**4/28 + 4*b**3/21 - b**2. Factor i(z).
-2*(z - 4)*(z - 1)**2/7
Let t(b) be the second derivative of -b**6/45 - b**5/20 + b**3/18 + 12*b. Solve t(z) = 0.
-1, 0, 1/2
Let n be 1/(-3) - 39/(-9). Determine a, given that -n*a**4 + 6*a**3 + 6*a**3 - 12*a**3 + 4*a**5 = 0.
0, 1
Let f = -10 - -14. Let p = f + 0. Factor 7*h**2 - p*h + 2*h**3 - 10*h**3 + 2*h**4 + 2*h + h**4.
h*(h - 1)**2*(3*h - 2)
Let n(x) be the third derivative of -x**7/735 + x**6/105 - x**5/70 - x**4/21 + 4*x**3/21 + 11*x**2. Let n(g) = 0. What is g?
-1, 1, 2
Let d(p) = -p - 2*p + 9*p - 6*p**2 - 11. Suppose 5*g = -3*c - 13, -3*c = c - 5*g + 64. Let k(a) = a**2 - a + 2. Let z(h) = c*k(h) - 2*d(h). Factor z(s).
s*(s - 1)
Let z(g) be the second derivative of g**7/105 + g**6/25 + g**5/50 - g**4/10 - 2*g**3/15 - 15*g. What is q in z(q) = 0?
-2, -1, 0, 1
Let b(j) = -15*j**2 - 9*j + 6. Let c(y) = 10*y**2 + 6*y - 4. Suppose -2*p + 6 = -8. Let x(v) = p*c(v) + 5*b(v). Let x(h) = 0. What is h?
-1, 2/5
Let v = 848/3 + -280. Solve 16/3 - 4/3*q**2 - 2/3*q**3 + v*q = 0 for q.
-2, 2
Let u(x) be the first derivative of -x**4 + 8*x**3/3 + 1. Factor u(f).
-4*f**2*(f - 2)
Let t be 25/(-15) - (-98)/30. Factor 0 - t*i - 10*i**3 - 8*i**2.
-2*i*(5*i + 2)**2/5
Let b(v) be the second derivative of -v**6/1620 + v**5/540 + v**3/2 + v. Let o(c) be the second derivative of b(c). Determine p so that o(p) = 0.
0, 1
Let q(c) be the third derivative of -c**8/2688 + c**7/5040 + c**6/1440 - c**5/60 + 6*c**2. Let x(u) be the third derivative of q(u). Factor x(g).
-(3*g - 1)*(5*g + 1)/2
Let f(d) be the third derivative of -d**5/210 + d**4/42 - d**3/21 - 9*d**2. Factor f(n).
-2*(n - 1)**2/7
Let i be (-4)/18 - 24/(-108). Let n(o) be the third derivative of 1/24*o**4 + 0*o + o**2 + 0 + 1/60*o**5 + i*o**3. Factor n(b).
b*(b + 1)
Let q = -1/83 - -113/2490. Let j(o) be the second derivative of q*o**3 - 2*o + 1/60*o**4 + 0 + 0*o**2. Factor j(w).
w*(w + 1)/5
Suppose 3*u = 0, -4*m - u = -11 - 9. Let t(q) = 3*q**2 - 11*q - 7. Let z(l) = -4*l**2 + 10*l + 6. Let c(d) = m*z(d) + 4*t(d). Factor c(y).
-2*(y - 1)*(4*y + 1)
Let i(y) be the first derivative of -y**8/112 - 2*y**7/35 - y**6/8 - y**5/10 + y**2/2 - 1. Let v(t) be the second derivative of i(t). Find q such that v(q) = 0.
-2, -1, 0
Suppose -27*c = 6*c - 66. Factor -c*b - 3 - 1/3*b**2.
-(b + 3)**2/3
Determine g so that -1/5*g**3 + 3/5*g**2 + 0*g + 0 = 0.
0, 3
Let g be (-15)/(-2) - 3/(-6). Let s be 3/((-2)/(g/(-30))). Solve -2/5*p + 2/5*p**3 - s + 2/5*p**2 = 0 for p.
-1, 1
Let o = 3 + -1. Let c(h) = 8*h**2 + 8*h - 7. Let v be c(1). Let -v*u + 1 + 81/4*u**o = 0. What is u?
2/9
Let d(j) be the first derivative of 3*j**6/16 - 3*j**5/5 + 21*j**4/32 - j**3/4 - 19. Factor d(y).
3*y**2*(y - 1)**2*(3*y - 2)/8
Let s(r) = 8*r**5 - 8*r**4 + 6*r**3 - 2*r. Let c(f) = 17*f**5 - 15*f**4 + 13*f**3 - 5*f. Let i(t) = -2*c(t) + 5*s(t). Find p, given that i(p) = 0.
0, 2/3, 1
Let t(b) be the third derivative of b**7/5040 + b**6/1440 + b**4/24 + 4*b**2. Let g(m) be the second derivative of t(m). Factor g(l).
l*(l + 1)/2
Let y(j) be the third derivative of 0*j - 1/30*j**5 + 0*j**3 - 1/24*j**4 + 1/336*j**8 - 3*j**2 + 0*j**6 + 1/105*j**7 + 0. Factor y(x).
x*(x - 1)*(x + 1)**3
Let r(i) be the third derivative of i**9/6048 - i**7/1680 - i**3/6 - 3*i**2. Let n(q) be the first derivative of r(q). Solve n(v) = 0 for v.
-1, 0, 1
Let m(k) = k**2 + 6*k + 7. Let x be m(-5). Factor -2*o**3 - 2*o**5 + o**4 + 3*o**4 + 2*o**2 - 2*o**x.
-2*o**3*(o - 1)**2
Let x(q) be the third derivative of q**8/420 + q**7/105 - 7*q**3/6 + 4*q**2. Let p(d) be the first derivative of x(d). Determine a so that p(a) = 0.
-2, 0
Suppose 2*q - 5*q = -5*p - 21, 15 = -5*p. Suppose 11*w**2 - 3*w**2 + 4*w**4 - 2*w**5 - 4 - q*w**5 + 8*w**3 - 4*w - 8*w**4 = 0. Calculate w.
-1, 1
Factor 3/5*f + 3/5*f**4 - 3/5*f**2 + 0 - 3/5*f**3.
3*f*(f - 1)**2*(f + 1)/5
Let c = -38 - -42. Let m(n) be the third derivative of 1/30*n**5 + 1/3*n**3 + 0*n - 1/6*n**c - 3*n**2 + 0. Let m(p) = 0. Calculate p.
1
Factor 45/4*g**3 - 39/4*g**2 + 3*g - 21/4*g**4 + 0 + 3/4*g**5.
3*g*(g - 4)*(g - 1)**3/4
Solve 3/2*u**3 + 17/2*u**2 + 11*u + 4 = 0.
-4, -1, -2/3
Let h(y) be the second derivative of -y**9/756 - y**8/140 - y**7/105 - y**3 - 6*y. Let o(g) be the second derivative of h(g). Factor o(m).
-4*m**3*(m + 1)*(m + 2)
Let g(y) be the second derivative of 3*y**5/10 - 5*y**4/4 - 2*y**3 + 9*y**2/2 + 3*y. Factor g(f).
3*(f - 3)*(f + 1)*(2*f - 1)
Let b be -1 - ((-12)/(-66) + 26/(-22)). Factor 0 - 1/6*t**5 - 1/3*t**4 - 1/6*t**3 + 0*t + b*t**2.
-t**3*(t + 1)**2/6
Let h(r) be the second derivative of r**7/42 - r**6/30 - r**5/4 + r**4/12 + 4*r**3/3 + 2*r**2 + 18*r. Suppose h(q) = 0. Calculate q.
-1, 2
Let l(t) = -2*t**4 + 4*t**3 + 2*t**2 - t. Let k(c) = 3*c**4 - 8*c**3 - 5*c**2 + c. Let d(w) = 3*k(w) + 5*l(w). Let d(i) = 0. What is i?
-2, -1, 0
Let q = -47 - -28. Let b = q + 19. Factor -2/5*t**3 + 0 + b*t**2 + 2/5*t.
-2*t*(t - 1)*(t + 1)/5
Let l be (-3 - -2)/(5/(-2)). Determine q, given that 0 - 2/5*q - l*q**2 = 0.
-1, 0
Let y(b) = b + 1. Let g be y(1). Suppose -5*i - g - 2*i - i**2 + 4*i = 0. What is i?
-2, -1
Let t(w) = w**3 - w**2 - 5*w - 3. Let y be t(3). Let d(q) be the first derivative of y*q - 1 - 1/12*q**3 + 0*q**2. What is s in d(s) = 0?
0
Factor 0 - 4/3*c - 2/3*c**2.
-2*c*(c + 2)/3
Let m(b) = b - 5. Let t be m(8). Factor 4*r**4 - 14*r + 8*r**5 + 14*r - 4*r**t.
4*r**3*(r + 1)*(2*r - 1)
Let t(s) be the third derivative of -1/6*s**4 + 6*s**2 + 1/30*s**6 + 0*s + 0*s**3 + 1/15*s**5 + 0 - 2/105*s**7. Factor t(d).
-4*d*(d - 1)**2*(d + 1)
Let b(w) be the third derivative of -w**6/30 + w**5/15 + 6*w**2. Factor b(d).
-4*d**2*(d - 1)
Let i(c) be the third derivative of 1/330*c**6 + 1/1155*c**7 + 0*c**4 + 0*c**3 + 0 + 1/330*c**5 + 2*c**2 + 0*c. Factor i(v).
2*v**2*(v + 1)**2/11
Factor -4/17 - 2/17*u + 2/17*u**3 + 4/17*u**2.
2*(u - 1)*(u + 1)*(u + 2)/17
Let b(j) be the first derivative of 3*j**5/5 - j**4/2 + j**3/3 - j - 3. Let u(z) = z**4 + z**2 - 1. Let h(y) = b(y) - u(y). Factor h(c).
2*c**3*(c - 1)
Let p be (2 - 2)/(-1) - 12/(-24). Solve 0 + 1/2*j**4 - 1/2*j**2 - p*j**3 + 1/2*j = 0 for j.
-1, 0, 1
Solve 2*g**3 + 2/5*g**4 + 18/5*g**2 + 14/5*g + 4/5 = 0 for g.
-2, -1
Let n(b) be the second derivative of -1/27*b**4 + 0*b**2 + 8*b + 1/27*b**3 - 1/30*b**5 + 0. Suppose n(s) = 0. Calculate s.
-1, 0, 1/3
Let q(x) be the third derivative of 1/630*x**7 + 1/360*x**6 + 0*x**5 + 0*x**4 + 0*x**3 + 0 + 0*x + x**2. Factor q(g).
g**3*(g + 1)/3
Let l be (-44)/(-32) - 5/(-40). Solve -l*m + 1/4*m**2 + 9/4 = 0.
3
Let i(w) be the third derivative of w**8/28 + 17*w**7/70 + w**6/2 + w**5/5 - 14*w**2. Factor i(z).
3*z**2*(z + 2)**2*(4*z + 1)
Let z(i) be the third derivative of -i**7/630 + i**5/30 - i**4/9 + i**3/6 + 17*i**2. Factor z(c).
-(c - 1)**3*(c + 3)/3
Let c = 133/6 - 43/2. Factor 2/3*y**3 - 2/3*y + 0 + 2/3*y**2 - c*y**4.
-2*y*(y - 1)**2*(y + 1)/3
Let u(z) = -z**3 + 7*z**2 + z - 9. Let h be u(7). Let t = h - -4. Solve -4*w + 1 + 0*w + t*w**2 + 1 = 0 for w.
1
Let m(l) be the first derivative of 6*l + 7*l**3 - 6 - 27/2*l**2. Factor m(c).
3*(c - 1)*(7*c - 2)
Let a(c) = -c**2 + 2*c - 1. Let r be a(-3). Let f be (3/2)/((-12)/r). Factor -2/9*l - 2/9*l**f + 0.
-2*l*(l + 1)/9
Let v(u) = -u**3 + 3*u + 2. Let o be v(2). Factor -2/5*d**5 - 4/5*d**4 + 0*d**2 + 0*d - 2/5*d**3 + o.
-2*d**3*(d + 1)**2/5
Let o(k) be the first derivative of 2*k**5/25 - 3*k**4/10 + 2*k**3/5 - k**2/5 - 6. Solve o(w) = 0 for w.
0, 1
Let s(n) = -n**3 + 4*n + 3. Let x be s(-1). Let l(c) be the third derivative of 0*c**3 + x + 1/36*c**4 - 1/180*c**6 + 0*c + 0*c**5 - 3*c**2. Factor l(y).
-2*y*(y - 1)*(y + 1)/3
Let v(o) be the first derivative of o**5/15 - 2*o**3/9 + o/3 + 9. Suppose v(u) = 0. What is u?
-1, 1
Let l(v) be the second derivative of 0 - 1/60*v**5 - 1/9*v**3 + 0*v**2 