*y**3 - 31*y**2 - 2*y + 24. Let x(h) = -h**4 - h**2 - 2*h. Let v(m) = n(m) - 4*x(m). Determine o, given that v(o) = 0.
-2, -1, 1, 4
Let g = 5/308 + 1073/308. What is m in -11/2*m**3 - 2*m**4 + g*m**2 - 3/2 + 11/2*m = 0?
-3, -1, 1/4, 1
Let a(u) = -5*u**2 + 451*u - 10127. Let d(b) = b - 2. Let i(l) = a(l) - d(l). What is z in i(z) = 0?
45
Suppose -5*p = -2*w + 21, 12 = 3*w - 2*p + p. Suppose 3*v = n + 13, 0*n + w*n = -3*v + 21. Find h such that -2/5*h + 0 - 2/5*h**n = 0.
-1, 0
Determine t so that 4279*t + 2*t**3 - 4279*t + 4*t**2 = 0.
-2, 0
Factor 47/5*l - 11/5*l**2 - 36/5.
-(l - 1)*(11*l - 36)/5
Determine h so that 1/3*h**3 + 17/3*h**2 + 0 + 16/3*h = 0.
-16, -1, 0
Suppose 124 = 4*l + 116. Factor 5/3*r**l + 1/3*r**3 + 0*r + 0.
r**2*(r + 5)/3
Let c(b) be the second derivative of b**8/20160 + b**7/7560 + 7*b**4/12 + 7*b. Let k(j) be the third derivative of c(j). Solve k(o) = 0 for o.
-1, 0
Suppose 0*w + 1 = w - 2*p, -5*w = 4*p - 19. Let z(r) be the second derivative of -2/3*r**2 - 1/60*r**5 + 0 - 4/9*r**w - 5/36*r**4 - 8*r. Solve z(q) = 0.
-2, -1
Let j be (-24)/(-504)*(-2)/24*-7. Let c(d) be the first derivative of 4/9*d + 9 - 1/9*d**3 + j*d**4 + 0*d**2. Determine n, given that c(n) = 0.
-1, 2
Let h(m) be the second derivative of 1/9*m**3 - 1 + 9*m + 0*m**2 + 1/12*m**4 + 1/60*m**5. Find j such that h(j) = 0.
-2, -1, 0
Let i be ((-42)/63)/((-2)/6). Factor -i*x**5 + 6*x**5 - 4*x + 8*x**4 - 22*x**2 + 14*x**2.
4*x*(x - 1)*(x + 1)**3
Let u(y) be the first derivative of -2*y**6/3 + 24*y**5/5 - 11*y**4 + 8*y**3 - 161. Determine b so that u(b) = 0.
0, 1, 2, 3
Let l = -7/66 + 16/99. Let m(x) be the second derivative of -1/9*x**3 + 0 - l*x**4 + 0*x**2 - 2*x. Solve m(j) = 0 for j.
-1, 0
Let k(l) be the second derivative of l**4/24 + 9*l**3/2 - 55*l**2/4 - 176*l. Factor k(t).
(t - 1)*(t + 55)/2
Let o(w) be the second derivative of -20*w + 0*w**2 + 0 + 2/3*w**3 - 3/20*w**5 + 0*w**4 + 1/30*w**6. Suppose o(y) = 0. Calculate y.
-1, 0, 2
Let y(v) be the second derivative of -v**8/3360 + v**7/315 - v**6/90 + 13*v**4/12 - v. Let f(s) be the third derivative of y(s). Determine t so that f(t) = 0.
0, 2
Let p(i) = -i**3 + 3*i**2 - 18*i + 7. Suppose 13 = 9*a - 14. Let f(n) = -5*n**2 + 35*n - 15. Let u(y) = a*f(y) + 5*p(y). Determine x, given that u(x) = 0.
-2, 1
Suppose -2*k = -4, -2*u + 8 = -0*u - k. Let j(s) be the second derivative of 1/6*s**4 - 1/50*s**u + 0 - 5*s + 4/5*s**2 - 8/15*s**3. Factor j(y).
-2*(y - 2)**2*(y - 1)/5
Let o(s) be the first derivative of 34*s**3/11 - s**2 - 4*s/11 - 215. Factor o(a).
2*(3*a - 1)*(17*a + 2)/11
Let v = -27 - -29. Suppose -30 = -5*x + 5*y, 5*y = x - 4*x + v. Factor -5*b**3 + 2*b**4 + 4*b**2 - 4 + 11*b**3 + x.
2*b**2*(b + 1)*(b + 2)
Let g be (27 + -36)*5/(-9). Let d be -1 + 4/(g + -1). Solve d*v + 0 + 1/5*v**2 = 0 for v.
0
Let w(k) be the second derivative of 1/50*k**5 - 1/15*k**3 + 1/75*k**6 + 0*k**2 + 0 + 20*k - 1/30*k**4. Factor w(n).
2*n*(n - 1)*(n + 1)**2/5
Let b(s) be the second derivative of s**8/6720 - s**7/672 + s**6/360 - 5*s**3/2 - 11*s. Let w(m) be the second derivative of b(m). Factor w(f).
f**2*(f - 4)*(f - 1)/4
Let x(u) be the first derivative of 15/2*u**2 + 20*u + 13 - 5/3*u**3. Solve x(t) = 0.
-1, 4
Let q(l) = l**2 - 5*l - 6. Let d be q(6). Suppose d = -k - 4*k + 10. Find n, given that 10*n**4 - 5*n**4 - 47*n - 25*n**3 + 45*n**k + 10 + 12*n = 0.
1, 2
Let m = -157 - -164. Let v(w) be the third derivative of 0*w**6 + 0*w**4 + 0*w + 0*w**3 + 0 + 3*w**2 + 1/70*w**m - 1/20*w**5. Factor v(t).
3*t**2*(t - 1)*(t + 1)
Let z = -329/5 - -997/15. Let o(q) be the second derivative of 1/5*q**5 + 1/15*q**6 + 0*q**2 - 1/6*q**4 - z*q**3 - 7*q + 0. Suppose o(v) = 0. What is v?
-2, -1, 0, 1
Let s(l) be the second derivative of l**4/12 - 11*l**3/6 + 7*l**2 + 5*l. Let w be s(10). Suppose w*o**2 - 3 - 5*o**2 - 4*o + 1 - o**2 = 0. Calculate o.
-1
Let z(g) be the second derivative of g**3/3 - 10*g**2 + 5*g. Let d be z(10). Find o such that 2/5*o**5 + 0*o + d - 2/5*o**2 - 2/5*o**3 + 2/5*o**4 = 0.
-1, 0, 1
Suppose s - 17*s = 10*s. Let d(j) be the first derivative of 2/15*j**3 - 3/20*j**4 - 4 + 0*j**2 + 1/30*j**6 + 0*j + s*j**5. Suppose d(n) = 0. Calculate n.
-2, 0, 1
Let 49/3*a**2 + 40/3 + 26*a + 4*a**3 + 1/3*a**4 = 0. Calculate a.
-5, -4, -2, -1
Let y(p) = p**2 - 2*p - 12. Let d be y(5). Let g be 32/24 + 2/d. Factor 18*x - 2*x - 16 - 2*x**g + 2*x**2 - 4*x**2.
-4*(x - 2)**2
Factor 10*j + j**2 - 19*j + 43*j - 2*j**2 - 120 + 9*j.
-(j - 40)*(j - 3)
Suppose -1 - 7 = -2*r. Let h be 4*((-14)/4)/(-7). Factor -r + 2*j + 4 - j**h.
-j*(j - 2)
Solve 0 - 12/7*m - 39/7*m**3 + 36/7*m**2 + 18/7*m**4 - 3/7*m**5 = 0 for m.
0, 1, 2
Let f = -10 - -33. Let y = 25 - f. Factor -4/3*h**y + 8/3*h + 0.
-4*h*(h - 2)/3
Factor 2*h**2 + 83 + 40*h - 8*h + 6*h**2 - 55 - 4*h**2.
4*(h + 1)*(h + 7)
Let n = 415 - 1659/4. Factor 3/4*r**2 + 0*r - 1 - n*r**3.
-(r - 2)**2*(r + 1)/4
Let o(g) = 48*g**3 + 80*g**2 - 37*g - 71. Let b(q) = -96*q**3 - 158*q**2 + 76*q + 143. Let y(a) = -4*b(a) - 7*o(a). What is x in y(x) = 0?
-5/4, 1
Suppose 0 = k + 4*k - 10. Factor 7 - k - 5 - 4*c**4.
-4*c**4
What is z in 8166*z**3 + 205*z**2 - 200*z + 8158*z**3 - 16329*z**3 = 0?
0, 1, 40
Let k(n) = -2*n. Let t be k(9). Let r = 18 + t. Factor 1/3*h - 1/3*h**3 + r + 0*h**2.
-h*(h - 1)*(h + 1)/3
Factor 7*c - 198*c**2 + 201*c**2 + 20 - 3*c - 8 + 11*c.
3*(c + 1)*(c + 4)
Let v(i) be the first derivative of 4/3*i**3 + 0*i - 20 + 2*i**2. Find s, given that v(s) = 0.
-1, 0
Let j(m) = 5*m**5 - 5*m**4 - 6*m**3 + 6*m**2 - 6*m + 6. Let g(c) = -c**5 + c**4 + c**3 - c**2 + c - 1. Let w(k) = 6*g(k) + j(k). What is d in w(d) = 0?
0, 1
Let l(t) be the third derivative of 1/630*t**7 - 1/180*t**5 + 0*t**6 + 0*t**4 + 9*t**2 + 0*t + 0 + 0*t**3. Factor l(h).
h**2*(h - 1)*(h + 1)/3
Let z(o) be the second derivative of -o**4/30 + 28*o**3/15 - 196*o**2/5 - 50*o. Suppose z(r) = 0. Calculate r.
14
Let v(o) be the first derivative of -2*o**5/5 + 2*o**4 - 2*o**3 + 92. Factor v(i).
-2*i**2*(i - 3)*(i - 1)
Suppose 4*w + 7 - 14 = l, 2*w = -l + 5. Suppose -3*t = -2*i + w, -5*t = -4*i - i + 10. Factor -1/5*o**t - 1/5*o**3 + 1/5*o**4 + 0 + 1/5*o.
o*(o - 1)**2*(o + 1)/5
Determine l so that -135*l**2 + 969*l - 3*l**3 + 5*l**3 + 111*l - 2160 + 3*l**3 = 0.
3, 12
Let t(f) be the first derivative of 1/90*f**5 - 1/135*f**6 + 0*f**3 + 0*f**4 + 0*f**2 + 3*f - 4. Let v(u) be the first derivative of t(u). Factor v(g).
-2*g**3*(g - 1)/9
Let b(r) be the third derivative of 4*r**7/105 - 11*r**6/30 + 13*r**5/15 - 2*r**4/3 - 10*r**2 + 4*r. Factor b(a).
4*a*(a - 4)*(a - 1)*(2*a - 1)
Find f such that -60/11*f**2 - 12/11 + 58/11*f + 14/11*f**3 = 0.
2/7, 1, 3
Suppose 218 = 50*c - 32. Let i(r) be the third derivative of 11*r**2 + 2/15*r**3 + 0 - 1/50*r**c + 1/12*r**4 + 0*r. Factor i(d).
-2*(d - 2)*(3*d + 1)/5
Let s = -27/61 + 2297/366. Let f = 16820 + -100885/6. Let -5/3*n**3 + s*n**4 + 5/3*n - f*n**2 + 0 = 0. What is n?
-1, 0, 2/7, 1
Let z(s) = -2*s**3 + 2*s**2 + 4*s + 6. Let d(q) = 4*q**3 - 3*q**2 - 7*q - 13. Let i(c) = 6*d(c) + 13*z(c). Solve i(h) = 0.
-1, 0, 5
Let a(b) = -2*b**2 - 1. Let t(z) = 6*z**2 - 32*z + 98. Let o(q) = -2*a(q) - t(q). Determine v so that o(v) = 0.
4, 12
Let w(d) be the first derivative of -d**2 - 2*d - 1/24*d**4 - 9 + 1/3*d**3. Let z(h) be the first derivative of w(h). Factor z(m).
-(m - 2)**2/2
Let u(m) = -3*m**3 - 76*m**2 - 10*m. Let t(x) = 12*x**3 + 303*x**2 + 45*x. Let k(f) = 2*t(f) + 9*u(f). Solve k(h) = 0.
-26, 0
Let u = 5264 + -10527/2. Factor -1/2*h + 0 + u*h**2.
h*(h - 1)/2
Factor 8 - 8*z**2 + 8*z - 8 + 33*z - 13*z - 24.
-4*(z - 2)*(2*z - 3)
Let q be -15 - 2578/(-168) - 4/16. Solve 2/21*f**2 - 2/21*f**4 + 0 + 2/21*f**5 + 0*f - q*f**3 = 0.
-1, 0, 1
Factor -18*f**2 - 5*f**3 - 15*f - 4 - 30*f - 32*f**2 + 4.
-5*f*(f + 1)*(f + 9)
Let p be (-46 - -49) + (2 - 1). Let t(i) be the second derivative of -1/100*i**5 - 1/210*i**7 + 0 + 0*i**2 - 4*i + 0*i**3 + 1/75*i**6 + 0*i**p. Factor t(f).
-f**3*(f - 1)**2/5
Let p(o) be the second derivative of 0 - 1/2*o**2 + 0*o**3 + o - 1/12*o**4 + 1/60*o**5. Let l(x) be the first derivative of p(x). Factor l(j).
j*(j - 2)
Suppose 2028*m + 26*m**2 + 1/9*m**3 + 52728 = 0. Calculate m.
-78
Let q = -61 + 197. Factor -g**3 + 136*g - q*g.
-g**3
Let n be (-11)/10 - (-36)/(-192)*-8. Let w = -8 + 8. 