*s**2 - 200*s - 80. Let o(d) = 3*d**4 + 100*d**3 + 330*d**2 + 400*d + 160. Let l(m) = -3*o(m) - 7*u(m). Factor l(f).
5*(f + 1)**2*(f + 4)**2
Let w be (-19)/(-30) - (-2)/(-15). Factor 1/2*x**2 + 0 - w*x**3 + 0*x.
-x**2*(x - 1)/2
Factor 2*m**2 + 200 + 14*m + 16*m + 10*m.
2*(m + 10)**2
Let b(y) be the first derivative of y**4/16 + y**3/6 + 6. Factor b(l).
l**2*(l + 2)/4
Solve 5/4*k**2 - 3/4*k**4 + k**3 + 0 - 1/2*k = 0.
-1, 0, 1/3, 2
Let g(t) be the second derivative of t**8/1120 - t**7/630 - t**4/12 + t. Let x(m) be the third derivative of g(m). Factor x(o).
2*o**2*(3*o - 2)
Suppose -20 = 2*m - 7*m. Suppose -35 - 221 = -m*h. Determine z so that -4 - 40*z - h*z**3 - 117*z**2 - 35*z**3 + 18*z**3 = 0.
-1, -2/9
Let u(r) be the first derivative of -r**4/30 + 2*r**3/15 + 4*r + 1. Let x(t) be the first derivative of u(t). Suppose x(h) = 0. Calculate h.
0, 2
Let d(k) be the first derivative of 2/9*k**2 - 1/9*k**4 - 2/9*k - 2 + 2/27*k**3. Factor d(b).
-2*(b - 1)*(b + 1)*(2*b - 1)/9
Let g = 1/3 + -1/4. Let v(f) be the third derivative of 1/120*f**6 + 0*f**5 + 0*f - 2*f**2 + 0 - g*f**3 + 1/420*f**7 - 1/24*f**4. What is a in v(a) = 0?
-1, 1
Let z(c) be the third derivative of -1/21*c**7 - 1/30*c**5 + 1/6*c**4 + 0 + 0*c**3 + 11*c**2 - 2/15*c**6 + 0*c. Solve z(k) = 0 for k.
-1, 0, 2/5
Let o = -13 - -13. Suppose o = -0*n + n. Determine k, given that 0*k - 2/3*k**2 + n = 0.
0
Let s = 12 - 8. Factor 0*k**5 - 6*k**5 + s*k**4 - 2*k**3 + 4*k**5.
-2*k**3*(k - 1)**2
Let l = 14 - 14. Let j(p) be the first derivative of 2/15*p**5 - 2 + 1/27*p**6 + 2/27*p**3 + 0*p**2 + l*p + 1/6*p**4. Factor j(f).
2*f**2*(f + 1)**3/9
Let f(d) be the second derivative of -d**7/28 + d**6/5 - 3*d**5/10 - d**4/4 + 5*d**3/4 - 3*d**2/2 + 7*d. Let f(v) = 0. What is v?
-1, 1, 2
Let v be 3*(3 + -6 - -4). Suppose 0 = -2*n - 0*n + v*t + 1, -4*n + 9 = t. What is c in 13*c - 7*c - 2*c**2 - 10*c**n + 6 + 15*c = 0?
-1/4, 2
Factor 0*p - 1/5*p**3 + 0 + 1/5*p**2.
-p**2*(p - 1)/5
Let o(x) be the third derivative of x**8/168 + x**7/105 - x**6/20 - x**5/6 - x**4/6 + 5*x**2. Find j, given that o(j) = 0.
-1, 0, 2
Let v(t) be the third derivative of t**2 + 1/70*t**5 - 2/21*t**4 + 0 + 0*t + 4/21*t**3. Let v(s) = 0. What is s?
2/3, 2
Let w be (6 + -6)/(6/(-3)). Factor 1/5*l**4 + 0 + 0*l**3 + 0*l + w*l**2.
l**4/5
Let d(z) be the second derivative of -z**4/114 + 5*z**3/57 - 6*z**2/19 - 30*z. Find m, given that d(m) = 0.
2, 3
Factor -38*a**3 - a**2 + 5*a + 18*a**3 + 21*a**3 - 3*a**2 - 2.
(a - 2)*(a - 1)**2
Let f(r) be the first derivative of -1/2*r**6 + 2*r**3 + 0*r**2 - 6/5*r**5 - 6 + 3/4*r**4 + 0*r. Find n, given that f(n) = 0.
-2, -1, 0, 1
Let m(h) be the first derivative of 1 + 0*h + 1/4*h**2 + 1/16*h**4 - 1/4*h**3. Let m(c) = 0. What is c?
0, 1, 2
Let w(p) be the second derivative of p**7/42 - p**6/15 + p**4/6 - p**3/6 + 29*p. Find x such that w(x) = 0.
-1, 0, 1
Let y = 8 + -6. Suppose -y*s = -s - 2. Factor 2*f**s + 2*f - f**2 - f.
f*(f + 1)
Let l = 379 + -374. Factor -1/5*d**l + 0*d**4 + 0 + 0*d + 0*d**2 + 0*d**3.
-d**5/5
Suppose -44*i = -39*i. Let n(b) be the first derivative of -1 + i*b + 2/5*b**3 + 1/10*b**4 + 2/5*b**2. Let n(z) = 0. What is z?
-2, -1, 0
Factor 0 + 1/3*v + 1/6*v**4 - 5/6*v**2 - 1/6*v**5 + 1/2*v**3.
-v*(v - 1)**3*(v + 2)/6
Let x(z) be the third derivative of 0 + 0*z - 3*z**2 - 1/12*z**4 + 0*z**3 + 1/60*z**5. Factor x(q).
q*(q - 2)
Let i(u) be the third derivative of u**5/20 - u**4/4 + u**3/2 - 3*u**2. Solve i(s) = 0.
1
Suppose 3 = 3*s + b, -7 = 2*b - 1. Suppose 0*j**3 + 5*j**s + 0*j**2 + 2*j**3 + 2*j - j**2 = 0. Calculate j.
-1, 0
Let h(c) be the third derivative of 0 + 0*c**3 - 7*c**2 + 0*c - 1/84*c**6 - 1/42*c**4 + 1/30*c**5. Factor h(t).
-2*t*(t - 1)*(5*t - 2)/7
Let v(h) = -h**3 + h**2 + 1. Let c(l) = l**4 - 8*l**3 + 7*l**2 + 6. Let d(y) = -c(y) + 6*v(y). Factor d(i).
-i**2*(i - 1)**2
Let x(l) = -l**2 + 4*l + 12. Let i be x(6). Suppose -1/2*m + 1/2*m**2 + i = 0. Calculate m.
0, 1
Let z(b) be the first derivative of -14*b**3/3 - 23*b**2 - 12*b + 30. Factor z(p).
-2*(p + 3)*(7*p + 2)
Let x(p) = 6*p + 31. Let r be x(-5). Let l(g) be the first derivative of 2/9*g**3 + 2/3*g**2 + 2/3*g - r. What is h in l(h) = 0?
-1
Suppose 147*n = 143*n + 16. Determine a, given that -2/11*a**5 + 0 - 6/11*a**3 - 2/11*a**2 + 0*a - 6/11*a**n = 0.
-1, 0
Suppose -7*y + 3 + 11 = 0. Let l(u) be the second derivative of -1/4*u**y + u + 0 - 1/48*u**4 + 1/8*u**3. What is m in l(m) = 0?
1, 2
Let j(w) be the first derivative of w**6/45 + 2*w**5/25 + w**4/10 + 2*w**3/45 - 14. Factor j(a).
2*a**2*(a + 1)**3/15
Let c be (-2)/3*-9*3. Let m be 1 + (c/15)/(-2). Find i such that 0 + 3/5*i**2 + i**3 - m*i = 0.
-1, 0, 2/5
Let c(t) be the second derivative of 3/2*t**2 + 0 + 2*t - 9/20*t**6 + 7/8*t**4 - 11/4*t**3 + 33/40*t**5. Let c(y) = 0. What is y?
-1, 2/9, 1
Let u(n) be the first derivative of 3 - 1/9*n**3 - 4/3*n - 2/3*n**2. Determine a so that u(a) = 0.
-2
Let g = 411 - 2869/7. Find x, given that -4/7 - g*x**2 - 2/7*x**3 - 10/7*x = 0.
-2, -1
Let a be (-36)/(-18) - (0 + (-2)/(-3)). Factor 4/3 - 2/3*h**3 - h**2 + 1/3*h**4 + a*h.
(h - 2)**2*(h + 1)**2/3
Suppose 2*u - 7 = 3*d, -2*d = -5*u - 5*d + 7. Suppose 3*q - 3*l - l = 24, -5*l = 15. Factor 2*r**2 - u*r**2 + 9*r**4 - q*r**2.
r**2*(3*r - 2)*(3*r + 2)
Let i be (-4)/14 + (-74)/(-14). Suppose -33 = -2*m + i*t - 6, -5*t + 3 = 3*m. Factor 5*r**4 - r**3 - 2*r**2 + r - m*r**4 + 3*r**2.
-r*(r - 1)*(r + 1)**2
Factor -5*i + 3*i**4 + 3*i**3 + 2*i + 0*i**2 - 3*i**2.
3*i*(i - 1)*(i + 1)**2
Suppose -7*c = -3*c. Let o(u) be the first derivative of 1/9*u**3 + c*u + 1/5*u**5 + 1/4*u**4 + 0*u**2 - 2 + 1/18*u**6. Factor o(q).
q**2*(q + 1)**3/3
Let r be -1*8/6*9/(-18). Factor r*f**2 + 0 + 0*f.
2*f**2/3
Let n(k) be the first derivative of -5*k**6/3 - 4*k**5/5 + 5*k**4 + 8*k**3/3 - 5*k**2 - 4*k + 14. Solve n(i) = 0.
-1, -2/5, 1
Factor 0*b + 3/7*b**3 + 3/7*b**2 + 0.
3*b**2*(b + 1)/7
Let -140*i**4 - 5*i**2 + 40*i**4 - i**2 - 10*i**2 + 80*i**3 = 0. Calculate i.
0, 2/5
Let s(u) = -u**4 + u**3 + u**2 - 1. Let n(h) = -h**5 + 3*h**3 - 2. Let k(l) = -3*n(l) + 6*s(l). Factor k(j).
3*j**2*(j - 2)*(j - 1)*(j + 1)
Suppose 0 = 5*d - 9*d - 2*f + 16, -f = -2*d. Suppose -1 + 3/2*v - 1/2*v**3 + 0*v**d = 0. Calculate v.
-2, 1
Let s(n) be the third derivative of -1/3*n**3 - 5/24*n**4 - 1/15*n**5 - 1/120*n**6 + 0 + 2*n**2 + 0*n. Suppose s(g) = 0. Calculate g.
-2, -1
Let p = -1528/725 - -53/29. Let g = 51/175 - p. What is f in 2/7*f - 2/7*f**2 + g = 0?
-1, 2
Let m = 2/2629 - -55201/10516. Let -m*f**3 - 9*f**2 + 3/2 - 9/4*f = 0. What is f?
-1, 2/7
Let j be ((-13)/117)/((-6)/27). Suppose 1/2*c**4 - c**3 + 1/2*c**5 + j - c**2 + 1/2*c = 0. Calculate c.
-1, 1
Factor 22/5*c + 8/5*c**2 - 6/5.
2*(c + 3)*(4*c - 1)/5
Let s(l) = l**3 + 10*l**2 + l + 3. Let c be s(-10). Let k = c - -11. Determine d so that 2*d**2 + 0*d**2 + 17*d**k + 9*d**3 + 5*d**5 - 5*d**4 = 0.
-1, -2/5, 0
Let r(a) be the second derivative of a**5/15 - 2*a**3/3 + a**2/2 - 10*a. Let u(k) be the first derivative of r(k). Solve u(l) = 0 for l.
-1, 1
Let k(v) = -60*v**5 + 99*v**4 + 10*v**3 - 93*v**2 + 40*v - 6. Let d(p) = -p**3 - p. Let t(j) = 5*d(j) - k(j). Determine w so that t(w) = 0.
-1, 1/4, 2/5, 1
Suppose -5*n = 4*s - 6, 7 = -2*n + 3. Suppose 14 + 1 = 5*b. Let v(k) = -k**2 - 2*k + 2. Let y(g) = g**2 + 2*g - 3. Let p(m) = b*y(m) + s*v(m). Factor p(q).
-(q + 1)**2
Let v be ((-12)/3)/(-16) - (-4)/112. Factor 2/7*o - 2/7 - 2/7*o**3 + v*o**2.
-2*(o - 1)**2*(o + 1)/7
Let c be 11/33 + (-2)/6. Solve c*r + 2*r - 3*r**2 - 2*r = 0.
0
Let k(t) be the second derivative of t**5/20 + 5*t**4/12 + 4*t**3/3 + 2*t**2 - 37*t. Determine y, given that k(y) = 0.
-2, -1
Let b(t) be the second derivative of -t**6/160 - t**5/80 + t**4/32 + t**3/8 - t**2 + 2*t. Let c(z) be the first derivative of b(z). Factor c(u).
-3*(u - 1)*(u + 1)**2/4
Let d(z) be the first derivative of 3*z + 3 + 1/24*z**4 + 1/2*z**2 - 1/4*z**3. Let x(u) be the first derivative of d(u). Find c, given that x(c) = 0.
1, 2
Suppose 13*k**4 - 104*k + 149*k + 10 + 70*k**3 + 8*k**4 + 80*k**2 + 9*k**4 + 5*k**5 = 0. Calculate k.
-2, -1
Suppose -1 = -4*o + 3*o. Suppose 4*k = 2*t + 20, 2*t = 2*k + o - 13. Factor -2/3*m**3 + 1/3*m**5 + 0*m**2 + 1/3*m + 0*m**k + 0.
m*(m - 1)**2*(m + 1)**2/3
Let y(q) = 20*q**3 + 28*q**2 - 8*