 + 1)**2/6
Let c(s) be the third derivative of -3*s**7/14 - 11*s**6/24 - s**5/6 + 8*s**2. Determine x so that c(x) = 0.
-1, -2/9, 0
Let k(z) be the second derivative of z**9/22680 - z**8/2016 + 2*z**7/945 - z**6/270 - z**4/12 - 4*z. Let r(i) be the third derivative of k(i). Factor r(c).
2*c*(c - 2)**2*(c - 1)/3
Suppose -4*x - 2*q + 16 = 0, 2*q + 14 = 5*x + 3*q. Let s(d) = 22*d + 47. Let y be s(-2). Factor -1/2*p**x - p**y + 1/2 + p.
-(p - 1)*(p + 1)*(2*p + 1)/2
Factor 0 - 1/3*j**2 - 2/3*j.
-j*(j + 2)/3
Suppose f - 220 = -2*v, -6*v = -3*v - 4*f - 352. Determine o so that -58*o**3 + 58 - 154*o**3 - 16*o - 80*o**4 - 58 - v*o**2 = 0.
-2, -2/5, -1/4, 0
Determine i, given that -2*i - 5/3 - 1/3*i**2 = 0.
-5, -1
Let c(f) be the third derivative of f**11/1829520 + f**10/415800 - f**5/20 + 3*f**2. Let g(a) be the third derivative of c(a). Let g(d) = 0. What is d?
-2, 0
Let a(h) be the first derivative of 1/12*h**3 + 1/16*h**4 - 2 + 0*h + 0*h**2. Factor a(r).
r**2*(r + 1)/4
Let r = 13 - 8. What is t in -3 + t**2 + t + r*t + 12 = 0?
-3
Let s = 5 + -3. Suppose -3*i + 23 = 2*w + 2*i, -2 = w - 2*i. Factor 0*t**s + 3*t**2 - 32*t**4 + 18*t**3 + w*t**3 + 14*t**5 - 7*t**2.
2*t**2*(t - 1)**2*(7*t - 2)
Let h be 2*(-3)/9*-3. Let q be 0 - (-3 - (h + -2)). Factor 2/3*r - 2/3*r**q + 4/3*r**2 - 4/3.
-2*(r - 2)*(r - 1)*(r + 1)/3
Let k = -13/705 + 4/47. Let b(t) be the first derivative of 0*t**2 - 2/15*t**3 + 3/10*t**4 + 2 + 0*t + k*t**6 - 6/25*t**5. Factor b(w).
2*w**2*(w - 1)**3/5
Let f(z) be the third derivative of -1/120*z**5 + 0*z - 3*z**2 + 0*z**3 + 0*z**4 + 0 + 1/240*z**6. Factor f(g).
g**2*(g - 1)/2
Factor 0*b + 0 + 1/4*b**3 + 1/2*b**2.
b**2*(b + 2)/4
Let y = -358 - -3942/11. Factor 0 - 2/11*r**3 - y*r + 6/11*r**2.
-2*r*(r - 2)*(r - 1)/11
Let d = -9 - -14. Let t be -4*(2/4 - 1). Suppose -61*w**4 + 52*w**4 + 2*w**t + 3*w**5 + 9*w**3 - d*w**2 = 0. What is w?
0, 1
Suppose f + 0*o + 4*o + 33 = 0, -2*f - 54 = 5*o. Let h be (f/170)/((-2)/15). Let 0*r**3 + 0*r - 3/4*r**2 + 0 + h*r**4 = 0. What is r?
-1, 0, 1
Let z(a) = -a**2 - 4*a + 7. Let y be z(-5). Factor 2*d**3 + 4*d**2 + 0*d - 2*d**2 - 6*d**2 + y*d.
2*d*(d - 1)**2
Let z(j) = -j**2 - 3*j - 2. Let x(q) = -7 + 5 + 3 + q**2 + q. Let f(y) = 6*x(y) + 3*z(y). Suppose f(a) = 0. Calculate a.
0, 1
Suppose -2/9*n + 2/9*n**3 + 0 + 0*n**2 = 0. What is n?
-1, 0, 1
Suppose 4*y + 2*r - 17 = -5, r = -y + 4. Let q(i) be the second derivative of -3/20*i**5 + 0*i**y + 1/4*i**4 + i - 1/6*i**3 + 1/30*i**6 + 0. Factor q(t).
t*(t - 1)**3
Let g(a) be the first derivative of a**5/5 - a**4/12 - 4*a**3/3 + 2*a**2/3 - 24. Factor g(i).
i*(i - 2)*(i + 2)*(3*i - 1)/3
Let z = 4 + -2. Suppose 4*r**3 - r + r**2 + 1 - z - 3*r**3 = 0. What is r?
-1, 1
Suppose x - 5 = -2. Let y be (-4)/(-32) + (-4 + 9)/(-40). Solve -2/3*o + y - 1/3*o**5 - 1/3*o**4 + 1/3*o**2 + o**x = 0 for o.
-2, -1, 0, 1
Suppose 0 = 9*s - 14*s. Let k(u) be the second derivative of s - 1/3*u**2 - 2*u - 1/6*u**3 - 1/36*u**4. Solve k(v) = 0.
-2, -1
Let x(r) be the third derivative of -r**5/12 + 25*r**4/24 - 10*r**3/3 + 57*r**2. Suppose x(n) = 0. Calculate n.
1, 4
Let y(h) = 4*h**2 - 6*h**2 - 5*h**3 - 3 - 4*h**2 - h**3. Let l(d) = d**4 + d**3 + d**2 + d + 1. Let u(n) = 3*l(n) + y(n). Solve u(o) = 0.
-1, 0, 1
Suppose 0 = 2*f - 3*n - 4, -3*n + 4 = 2*f - 4*n. Suppose -3*p + 24 = 3*j, 0*p - 13 = 4*p - 5*j. Factor f*w**4 - w**5 - 2*w**4 - w + 2*w**p.
-w*(w - 1)**2*(w + 1)**2
Let b(t) be the third derivative of t**7/315 + t**6/45 + 2*t**5/45 - 24*t**2 + 1. Find k such that b(k) = 0.
-2, 0
Let z(l) be the first derivative of 1 + 0*l - 4/21*l**3 + 2/35*l**5 + 1/14*l**4 + 0*l**2. Determine y so that z(y) = 0.
-2, 0, 1
Let x(p) = -p**3 - 3*p**2 + 2*p - 4. Let w be x(-4). Factor 6*r**w - 4*r**4 + 2*r**2 + 3*r**4 + 8*r**3 + r**5 + 2*r**2.
r**2*(r + 1)*(r + 2)**2
Let i(x) be the first derivative of -1/7*x**2 - 3/14*x**4 + 3 - 2/35*x**5 + 0*x - 2/7*x**3. Factor i(l).
-2*l*(l + 1)**3/7
Let u be (-3 + (-3)/(-3))*24/(-84). Factor 0*a**2 - 2/7*a**3 + u + 6/7*a.
-2*(a - 2)*(a + 1)**2/7
Let f(z) = 6*z**2 - 3*z - 1. Let n be f(1). Let r(c) be the second derivative of n*c + 1/110*c**5 + 1/66*c**4 + 0*c**2 + 0*c**3 + 0. Factor r(m).
2*m**2*(m + 1)/11
Let l(t) be the second derivative of -t**5/20 - t**4/12 + t**3/6 + t**2/2 + 2*t. Solve l(x) = 0 for x.
-1, 1
Let s(f) be the first derivative of -1/6*f**4 - 2/9*f**3 - 7 + 0*f**2 + 0*f. Factor s(m).
-2*m**2*(m + 1)/3
Let v be 1 + -2 + -1 - -4. Factor -3 - 5*q**2 + v + 4*q**2 - 2*q.
-(q + 1)**2
Let k = 2/3 - 1/3. Let d(z) be the third derivative of 0*z + 1/15*z**6 - k*z**4 - 8/105*z**7 + 1/6*z**3 + 1/4*z**5 - 3*z**2 + 0. Suppose d(r) = 0. Calculate r.
-1, 1/4, 1
Suppose -m = -3*k + 46, -2*k - 5*m - 4 + 12 = 0. Let q be (-22)/(-56) + (-2)/k. Determine u so that q*u + 1/4*u**2 + 0 = 0.
-1, 0
Let y(d) = -3*d - 10. Let q be y(-4). Factor 2/7*v**q - 4/7 + 2/7*v.
2*(v - 1)*(v + 2)/7
Let w(d) = d + 10. Let m be w(-8). Factor -2*v - 5*v**3 + 4*v**3 - v**2 + m*v**3.
v*(v - 2)*(v + 1)
Let t(y) be the third derivative of -y**6/120 - y**5/20 - y**4/8 - y**3/6 + 3*y**2. Factor t(u).
-(u + 1)**3
Suppose 49 - 17 = 2*p. Find h such that -2*h**4 - 2*h**2 + p*h**4 + 18*h**3 + 6*h**2 = 0.
-1, -2/7, 0
Let l(x) be the first derivative of -x**4/8 + x**3/3 + x**2/4 - x + 5. Determine h so that l(h) = 0.
-1, 1, 2
Suppose 4*z = -4*c, -7*z = -4*c - 2*z + 45. Let -r**c - 11*r**3 + 5*r**3 + 9*r**4 - 2*r**5 = 0. Calculate r.
0, 1, 2
Let c(m) = 4*m**4 - 15*m**3 + 31*m**2 - 33*m + 8. Let j(p) = -12*p**4 + 44*p**3 - 92*p**2 + 100*p - 24. Let b(h) = -16*c(h) - 5*j(h). Factor b(s).
-4*(s - 2)*(s - 1)**3
Let w(a) be the first derivative of 2/27*a**3 + 1/9*a**2 + 1 + 0*a. Factor w(f).
2*f*(f + 1)/9
Let z = 26 + -14. Factor 18*x**3 - 9*x**4 - z*x**4 - 4*x**2 + 10*x**5 - 3*x**4.
2*x**2*(x - 1)**2*(5*x - 2)
Let -80 + 0*g**2 - 5*g**2 + 0*g**2 - 5*g - 35*g = 0. What is g?
-4
What is h in -5 + 2 - 8*h + 2*h - 3*h**2 = 0?
-1
Suppose -a - 30 = -33. Solve -1/2*l**a - 7/4*l - 1/4 + 9/4*l**5 + 15/4*l**4 - 7/2*l**2 = 0 for l.
-1, -1/3, 1
Let g(t) be the first derivative of -2*t**5/45 + t**4/9 - 2*t**2/9 + 2*t/9 - 5. Factor g(l).
-2*(l - 1)**3*(l + 1)/9
Let x(u) be the first derivative of -u**5/3 + 2*u**4/3 - u**3/9 - u**2/3 - 1. Suppose x(t) = 0. Calculate t.
-2/5, 0, 1
Let f = -226 - -1363/6. Solve -1/3 + f*x + 3/2*x**2 = 0 for x.
-1, 2/9
Let m(s) be the first derivative of s**6/6 + s**5/5 - s**4/4 - s**3/3 + 39. Factor m(q).
q**2*(q - 1)*(q + 1)**2
Let t(j) be the first derivative of j**3/8 - 3*j**2/8 + 20. Factor t(k).
3*k*(k - 2)/8
Let w = 11 + -9. Factor -8*u - 5 - 1 - 2*u**w - 4*u**2 + 4*u**2.
-2*(u + 1)*(u + 3)
Let p be 14/8 + (-2)/(-8). Suppose 3*v = p*v. Factor -3*u**2 + 3*u - 2 + v*u + 8.
-3*(u - 2)*(u + 1)
Suppose -1/5*g**2 + 1/5*g**4 - 2/5*g**3 + 2/5*g + 0 = 0. Calculate g.
-1, 0, 1, 2
Find t, given that 4*t + 4*t - 8*t**3 + 2*t**4 + 2*t**4 - 4 = 0.
-1, 1
Let m = 175 + -171. Solve 0*q**3 - 1/3*q**m - 2/3*q + 0 + q**2 = 0.
-2, 0, 1
Let y(u) be the third derivative of -u**8/100800 - u**7/25200 + u**5/15 - u**2. Let d(g) be the third derivative of y(g). Find v such that d(v) = 0.
-1, 0
Let i = 5 - 5. Factor 11*b**4 - 6*b**2 - 3*b**5 - b - 5*b**4 + 4*b + i*b**2.
-3*b*(b - 1)**3*(b + 1)
Let i(p) be the first derivative of -1/180*p**6 + 0*p + 0*p**4 - 1/90*p**5 - p**2 - 2 + 0*p**3. Let b(m) be the second derivative of i(m). Solve b(k) = 0 for k.
-1, 0
Let x(y) = y**2 - 7*y + 8. Let a be x(6). Let -6*c**a + 3 + 18*c**3 - 6*c**2 - 2 + 3 - 10*c = 0. Calculate c.
-2/3, 1/3, 1
Let c = 302/705 - 4/141. Factor -6/5*h + 6/5*h**3 + 2/5*h**2 - 4/5 + c*h**4.
2*(h - 1)*(h + 1)**2*(h + 2)/5
Let z(r) be the first derivative of r**7/5040 + r**6/540 + r**5/144 + r**4/72 - r**3/3 + 1. Let f(p) be the third derivative of z(p). Factor f(d).
(d + 1)**2*(d + 2)/6
Let l(f) be the second derivative of -2*f - 5/48*f**4 + 0 + 1/12*f**3 + 1/20*f**5 + 0*f**2 - 1/120*f**6. Suppose l(h) = 0. What is h?
0, 1, 2
Let v be (-2)/(-9) - 237/(-27). Let t be (24/v)/4*1. Factor 2/3*a**4 + 0 + 0*a**2 + 0*a - t*a**5 + 0*a**3.
-2*a**4*(a - 1)/3
Let c(r) be the second derivative of -4*r**2 - 1/6*r**4 + 5*r + 4/3*r**3 + 0. Find l, given that c(l) = 0.
2
Let i(g) be the first derivative of g**6/720 + g**5/360 - g**4/72 + 7*g**2/2 - 6. Let c(d) b