 be the second derivative of b**4/12 + b**3/6 - b**2/2 - 2*b. Let g be s(-3). Suppose g*r**4 + 2 - 7*r**4 - r**3 + 4*r - 3*r**3 = 0. What is r?
-1, 1
Let d(t) be the second derivative of t**5/35 + t**4/14 - t**3/7 - 2*t**2/7 - t. Factor d(h).
2*(h - 1)*(h + 2)*(2*h + 1)/7
Let s be (104/(-1771))/((-3)/(-15)). Let y = -2/253 - s. Let -y*r**3 - 6/7*r + 2/7 + 6/7*r**2 = 0. Calculate r.
1
Let y = 274 - 271. Factor 6/5*q**4 + 0 + 0*q + 0*q**2 + 3/5*q**5 + 3/5*q**y.
3*q**3*(q + 1)**2/5
Let k(h) be the second derivative of h**6/135 - h**5/30 + h**4/18 - h**3/27 + h. Factor k(m).
2*m*(m - 1)**3/9
Let x(i) = -i**2 - i. Let w(j) = -j. Let q(v) = 7*v**2 - 2*v + 1. Let p(m) = q(m) - 6*w(m). Let g(d) = -p(d) - 6*x(d). Suppose g(z) = 0. What is z?
1
Let s be 0/(((-3)/(-1))/3). Factor -4 + 0 + s + 9*v - 3*v**2 - 2.
-3*(v - 2)*(v - 1)
Let v = 142 + -140. Suppose -1/2*j**2 + 2*j - v = 0. What is j?
2
Suppose p = 2 + 4. Let s(n) = -n**3 + 7*n**2 - 7*n + 9. Let b be s(p). Let -2*i**5 + 2*i**b + i**4 - i**4 = 0. What is i?
-1, 0, 1
Suppose 0 = -4*v - 8, 4 = 4*u + 2*v - 0. Suppose u = 3*i - 7. Suppose -2*h**i + 3*h**4 - h**4 + 0*h**4 - 2*h**2 + 2*h**5 = 0. Calculate h.
-1, 0, 1
Let y be 0 + (1 - 3/3). Suppose -4*l + l + 3*f = y, 5*l = -4*f + 18. Factor x - 2*x**l + x**3 - x + x.
x*(x - 1)**2
Let v = -8 + -20. Let m = v + 32. Factor -4/5*h**3 + 0 + 6/5*h**m + 0*h - 2/5*h**2.
2*h**2*(h - 1)*(3*h + 1)/5
Let l = 11 + -9. Determine u, given that 1/3*u + 1/3*u**l + 0 = 0.
-1, 0
Suppose 2*u - 2*c = u - 4, 0 = -u - 4*c + 20. Factor 2*z**5 - u*z**4 + 0*z**5 + 2*z**4.
2*z**4*(z - 1)
Determine v, given that -v**2 + 1/2*v**4 - v**5 + 2*v**3 - v + 1/2 = 0.
-1, 1/2, 1
Let w(d) be the first derivative of -d**7/70 - d**6/40 - 2*d**2 + 10. Let j(i) be the second derivative of w(i). Solve j(c) = 0.
-1, 0
Let f(t) be the third derivative of t**5/180 + t**4/18 + 10*t**2. Suppose f(u) = 0. What is u?
-4, 0
Let k(d) = -d**3 - 6*d**2 - 5*d - 3*d**2 - 7 - 6*d**3. Let q(w) = 27*w**3 + 36*w**2 + 21*w + 27. Let f(o) = -15*k(o) - 4*q(o). Suppose f(v) = 0. Calculate v.
-1
Let l(a) be the second derivative of a**7/14 - a**6/40 - 3*a**5/10 + a**4/8 + a**3/2 - 3*a**2/8 + 12*a. Find g, given that l(g) = 0.
-1, 1/4, 1
Let y(f) be the first derivative of 4*f**3/15 - 4*f**2/5 - 4. Let y(d) = 0. Calculate d.
0, 2
Let w(g) = -g**3 - 1. Let q = -8 - -11. Let x(j) = 2*j**3 - 4*j**2 - 3*j + 3. Let b(l) = q*w(l) + x(l). Factor b(f).
-f*(f + 1)*(f + 3)
Let h = 14/9 - 11/9. Let z(g) be the first derivative of -2 + 4/9*g + 2/27*g**3 - h*g**2. What is d in z(d) = 0?
1, 2
Let r(t) = 80*t**5 - 1270*t**3 + 595*t**2 + 1565*t + 55. Let h(p) = -3*p**5 + 47*p**3 - 22*p**2 - 58*p - 2. Let i(u) = -55*h(u) - 2*r(u). Solve i(k) = 0 for k.
-3, -1, 0, 2
Let v(h) be the third derivative of 0*h - 5*h**2 + 0*h**3 + 0 + 1/8*h**4 - 1/20*h**5. Find n, given that v(n) = 0.
0, 1
Let l(c) be the second derivative of -c**6/600 - c**5/200 + c**4/20 - 2*c**3/3 - 6*c. Let d(t) be the second derivative of l(t). Factor d(z).
-3*(z - 1)*(z + 2)/5
Factor 18*k**2 - 6*k**3 + 26*k**3 - 5*k - 3*k**2.
5*k*(k + 1)*(4*k - 1)
Let p(k) be the third derivative of k**5/360 + k**4/72 + k**3/36 + 5*k**2. Factor p(r).
(r + 1)**2/6
Determine q, given that 0 + 0*q + 1/4*q**2 + q**3 = 0.
-1/4, 0
Suppose 5*h + 18 = 3*h. Let s(v) = -v**3 - 8*v**2 + 9*v. Let i be s(h). Factor -1/2*b**3 + 1/4*b + 0 + i*b**4 + 0*b**2 + 1/4*b**5.
b*(b - 1)**2*(b + 1)**2/4
Let a(d) = 8*d**4 - 7*d**3 - 3*d. Let l(v) = 9*v**4 - 6*v**3 - 4*v. Let z(j) = -4*a(j) + 3*l(j). What is m in z(m) = 0?
0, 2
Let x(h) be the first derivative of -h**5/20 + h**4/4 - h**3/2 + h**2/2 + h + 2. Let b(u) be the first derivative of x(u). Suppose b(n) = 0. What is n?
1
Let p(c) be the first derivative of c**4/10 - 4*c**3/15 - 3*c**2/5 - 3. Let p(i) = 0. Calculate i.
-1, 0, 3
Suppose 5*r = 3*r. Let o(i) be the first derivative of -1/5*i**5 - 2 + 0*i - 3/4*i**4 + 1/2*i**6 + 1/3*i**3 + r*i**2. Factor o(s).
s**2*(s - 1)*(s + 1)*(3*s - 1)
Let v(h) be the third derivative of -h**7/840 + h**6/120 + h**5/240 - h**4/24 + 23*h**2. Solve v(b) = 0 for b.
-1, 0, 1, 4
Let u(x) be the first derivative of -12*x**5/25 + x**4 - 8*x**3/15 + 4. Determine n so that u(n) = 0.
0, 2/3, 1
Factor -3/2*m**4 + 3/4*m**3 + 0*m**2 + 0 + 3/4*m**5 + 0*m.
3*m**3*(m - 1)**2/4
Let j(c) be the second derivative of -c**4/4 - 5*c**3/6 + c**2 - 10*c. Factor j(b).
-(b + 2)*(3*b - 1)
Factor -6*c**2 + 9/2*c**4 + 0*c**3 + 3/2*c**5 + 0*c + 0.
3*c**2*(c - 1)*(c + 2)**2/2
Let c(h) be the first derivative of h**6/105 - 3*h**5/70 + h**4/14 - h**3/21 - 2*h + 3. Let w(a) be the first derivative of c(a). Let w(n) = 0. What is n?
0, 1
Find y, given that -9/2*y**3 + 0 + 0*y**2 - 3*y**4 + 3/2*y = 0.
-1, 0, 1/2
Let w = -1 - -5. Let 5 - 14*v**4 - 22*v**2 - 5 + 32*v**3 + w*v = 0. Calculate v.
0, 2/7, 1
Let l(k) = -k**3 - k - 1. Let w(g) = -3*g**3 + 4*g**2 - 5*g - 5. Let m(o) = -5*l(o) + w(o). Suppose m(c) = 0. Calculate c.
-2, 0
Let k(z) be the first derivative of 5*z**3/6 + 5*z**2 + 10*z - 1. Factor k(l).
5*(l + 2)**2/2
Let q(a) be the first derivative of a**6/8 - 9*a**5/20 - 3*a**4/16 + 7*a**3/4 - 3*a + 5. Determine l so that q(l) = 0.
-1, 1, 2
Let x(k) be the first derivative of -7*k**6/720 + k**5/20 + k**4/12 + k**3/3 - 3. Let h(s) be the third derivative of x(s). Solve h(p) = 0.
-2/7, 2
Let g(k) be the first derivative of 3/16*k**4 + 0*k + 4 + 1/20*k**5 + 1/4*k**3 + 1/8*k**2. Factor g(s).
s*(s + 1)**3/4
Let t = 6767/9 - 751. Find i such that 8/3*i + 14/9*i**2 - t = 0.
-2, 2/7
Let a(o) be the first derivative of 0*o + 0*o**4 - 1/30*o**5 + 1/2*o**2 + 0*o**3 - 1. Let x(u) be the second derivative of a(u). Factor x(w).
-2*w**2
Let b(l) be the third derivative of -l**7/105 - l**6/12 - 3*l**5/10 - 7*l**4/12 - 2*l**3/3 + 14*l**2. Factor b(y).
-2*(y + 1)**3*(y + 2)
Let z(j) = -3*j**5 + 25*j**4 - 41*j**3 + 35*j**2 - 8*j. Let p(r) = -3*r**5 + 24*r**4 - 42*r**3 + 36*r**2 - 9*r. Let v(i) = 4*p(i) - 3*z(i). Factor v(h).
-3*h*(h - 4)*(h - 1)**3
Let g(x) be the first derivative of 0*x - 3/4*x**4 + 2/3*x**6 - 1/3*x**3 + 0*x**5 + 0*x**2 + 4. Let g(r) = 0. Calculate r.
-1/2, 0, 1
Let b(v) be the second derivative of -v**4/12 + v**3/2 - v**2 - 6*v. Suppose b(c) = 0. Calculate c.
1, 2
Factor -9/2*c - 15/4*c**3 + 0 - 51/4*c**2.
-3*c*(c + 3)*(5*c + 2)/4
Suppose 0 = -s - 5*p + 8, -2*s - p + 11 = 4*p. Let o be (6/8)/(2/24). Factor 7 - o - 2*h**4 + s*h**2 + 0*h**2 + h**2.
-2*(h - 1)**2*(h + 1)**2
Let y(b) be the first derivative of 0*b**4 + 2/3*b**3 + 1/15*b**6 - 1/5*b**5 - b**2 - 2 + 2*b. Let x(i) be the first derivative of y(i). Factor x(g).
2*(g - 1)**3*(g + 1)
Let q = 191/3 - 379/6. Factor -1/2*t**2 - q*t + 1.
-(t - 1)*(t + 2)/2
Let g(u) be the third derivative of 2*u**7/105 + u**6/15 - u**4/3 - 2*u**3/3 - 3*u**2. Let g(h) = 0. Calculate h.
-1, 1
Factor -3 + 4 - 2*q - 4*q + q**2 + 4*q.
(q - 1)**2
Suppose -4*i = -5*t - 23 - 222, 0 = 3*i + 15. Let r = -211/4 - t. Solve r*z + 0 - 1/4*z**3 + 0*z**2 = 0.
-1, 0, 1
Let x = 6 + -4. Factor x*a**2 + 2*a - 6*a - 5*a + 3*a.
2*a*(a - 3)
Factor -9*l - 16*l**3 + 14*l**4 + 7*l - 4*l**5 + l**3 + 10*l**2 - 3*l**3.
-2*l*(l - 1)**3*(2*l - 1)
Let r(z) be the third derivative of -z**7/1680 + z**6/320 - z**5/480 - z**4/64 + z**3/24 - 11*z**2. Determine s, given that r(s) = 0.
-1, 1, 2
Let h(m) be the first derivative of -m**6/900 + m**5/300 - m**3/3 + 2. Let z(o) be the third derivative of h(o). Let z(c) = 0. Calculate c.
0, 1
Let m = 28/39 + -5/13. Factor 4/3*u**3 + m*u**4 + 0*u + 0 + 4/3*u**2.
u**2*(u + 2)**2/3
Let p(y) be the first derivative of -2/27*y**3 - 1/27*y**6 + 0*y + 1/18*y**4 + 1 + 2/45*y**5 + 0*y**2. Determine w so that p(w) = 0.
-1, 0, 1
Let v be 225/210*(-1 - 52/(-20)). Factor 10/7*o**3 + 0 + v*o**2 + 2/7*o.
2*o*(o + 1)*(5*o + 1)/7
Suppose 25 = 5*f - 15. Let h be 6/4*f/6. Suppose h*m**4 + m**3 + 2*m - 2*m + m**5 = 0. Calculate m.
-1, 0
Suppose 3*t = 3*v + 36, -2*v = -3*t - 6 + 37. Suppose 3*x = -1 + t. Factor s**x - 8*s - 4 - 4 - 3*s**2.
-2*(s + 2)**2
Let h(j) be the first derivative of 5*j**3/3 - 15*j**2/2 + 10*j + 12. Suppose h(a) = 0. Calculate a.
1, 2
Let g be ((-1 - -1) + 0)/(-13 - -14). Determine y so that 1/2*y + g - 1/2*y**2 = 0.
0, 1
Let w(l) = -l**3 - 13*l**2 - 12*l. Let u(q) = -6*q**3 - 90*q**2 - 84*q. Let j(d) = 2*