**4 - 27/2*c**3 = 0.
-1, -2/9, 0, 1
Let s = 12 - 10. Factor 3*k + 21*k**s + 42*k**5 - 25*k**3 + 70*k**3 + 39*k**4 - 30*k**5.
3*k*(k + 1)**3*(4*k + 1)
Let y = -374 - -376. Let k(d) be the first derivative of -3/7*d**4 - 3/35*d**5 - 5/7*d**3 + 3 - 3/7*d**y + 0*d. What is o in k(o) = 0?
-2, -1, 0
Let w(v) = -v**2 - 5*v + 8. Let u be w(-6). Suppose -21 = -3*p + 3*t, 2*p + 4*t + 6 = u. Find k such that 0*k + 3/2*k**3 - 3*k**p + 3/2*k**5 + 0*k**2 + 0 = 0.
0, 1
Let g(u) be the second derivative of u**6/60 - u**5/20 - u**4/24 + u**3/6 + 22*u + 3. Suppose g(n) = 0. What is n?
-1, 0, 1, 2
Let g(v) = 3*v - 17. Let f be g(9). Factor 23*d**2 + f*d + 5 + 12*d**2 - 45*d**3 - 5.
-5*d*(d - 1)*(9*d + 2)
Determine b, given that -136/3 + 136/3*b**2 + 4/3*b**3 - 4/3*b = 0.
-34, -1, 1
Factor 2/3*h**2 + 10*h + 52/3.
2*(h + 2)*(h + 13)/3
Factor 18/17*f**2 - 24/17*f - 4/17*f**3 + 8/17.
-2*(f - 2)**2*(2*f - 1)/17
Suppose 9*g = 3*g + 18. Suppose -3*p**2 - 16*p**3 + 4 - 5*p**2 + 16*p - 10*p**4 + 12 - p**5 + g*p**4 = 0. What is p?
-2, 1
Let w(x) = 8*x**3 + 75*x**2 - 290*x + 117. Let y(m) = -7*m**3 - 75*m**2 + 289*m - 118. Let d(l) = -5*w(l) - 6*y(l). Let d(t) = 0. Calculate t.
-41, 1/2, 3
Let y = -20 - -22. Let q(l) = -l**2 - 17*l + 18. Let m(k) = -6*k + 6. Let t(a) = y*q(a) - 7*m(a). Determine j so that t(j) = 0.
1, 3
Let p(t) = 10*t**2 + 15*t - 4. Let d(g) = -9*g**2 - 12*g + 1. Let b(c) = -9*c**2 - 11*c. Let u(y) = 2*b(y) - 3*d(y). Let l(f) = -5*p(f) + 6*u(f). Factor l(j).
(j + 2)*(4*j + 1)
Let o(r) = 6*r**3 - 22*r**2 - 55*r - 34. Let d(y) = -4*y**3 + 15*y**2 + 37*y + 23. Let b(l) = -7*d(l) - 5*o(l). Factor b(g).
-(g + 1)**2*(2*g - 9)
Let v(h) be the second derivative of -h**5/5 - h**4 + 6*h**3 + 54*h**2 + h + 32. Factor v(k).
-4*(k - 3)*(k + 3)**2
Let z(j) be the third derivative of 0*j - 1/180*j**5 + 0*j**3 + 0 - 12*j**2 + 1/630*j**7 + 1/360*j**6 - 1/72*j**4. Factor z(w).
w*(w - 1)*(w + 1)**2/3
Let g(s) be the third derivative of 4*s**7/1365 - 3*s**6/260 + s**5/65 - s**4/156 - s**2 + 7*s. Let g(i) = 0. Calculate i.
0, 1/4, 1
Let j(d) = -12*d**3 + 2024*d**2 - 112896*d + 2107384. Let f(w) = 8*w**3 - 1349*w**2 + 75264*w - 1404923. Let h(l) = -8*f(l) - 5*j(l). Let h(x) = 0. What is x?
56
Let o(c) be the third derivative of 0*c - 14*c**2 + 0 - 1/30*c**6 + 1/6*c**4 + 0*c**3 + 1/15*c**5 - 2/105*c**7. Factor o(f).
-4*f*(f - 1)*(f + 1)**2
Let t(z) be the first derivative of 1/30*z**5 + 1/6*z - 1/12*z**4 + 1/36*z**6 - 25 + 1/12*z**2 - 1/9*z**3. Find y, given that t(y) = 0.
-1, 1
Suppose -21 + 1844*k**3 + 736*k + 45*k**5 + 1760*k**2 + 253 + 753*k**4 - 39 - 81 = 0. What is k?
-14, -1, -2/3, -2/5
Suppose -5*r + r = 2*h + 64, -r = -4. Let w be -3 - h/(1 - -4). Let 0*x - 14/3*x**4 + 0*x**2 - 4*x**w - 4/3*x**3 + 0 = 0. What is x?
-2/3, -1/2, 0
Let q be (-2)/(-9) + 48566/882. Let c = q + -55. Determine f so that -c*f + 0 + 2/7*f**2 = 0.
0, 1
Let r = -25 + -3. Let c be (-21)/r*(3 - -1). Factor 4/3*z + 4/3 - 4/3*z**2 - 4/3*z**c.
-4*(z - 1)*(z + 1)**2/3
Let v(s) be the first derivative of -2*s**5/65 + s**4/13 + 40*s**3/39 + 24*s**2/13 + 517. Factor v(w).
-2*w*(w - 6)*(w + 2)**2/13
Let c(z) be the first derivative of z**5/20 + z**4/18 - z**3/6 - z**2/3 - 2*z - 10. Let l(g) be the first derivative of c(g). Factor l(u).
(u - 1)*(u + 1)*(3*u + 2)/3
Let j(x) be the second derivative of 10*x - 1/6*x**4 + 3*x**2 + 0 - 2/3*x**3. Factor j(o).
-2*(o - 1)*(o + 3)
Let s(l) be the first derivative of l**6/45 - 13*l**5/120 + 11*l**4/72 - l**3/18 - l - 14. Let j(h) be the first derivative of s(h). Factor j(z).
z*(z - 2)*(z - 1)*(4*z - 1)/6
Let f(k) = -k**2 - 31*k - 121. Let i(w) = -w. Let o(g) = 4*f(g) - 36*i(g). Solve o(j) = 0.
-11
Factor 11*w**2 - 2*w**3 - 52 + 54*w**2 + 102*w - 113*w**2.
-2*(w - 1)**2*(w + 26)
Find r such that 4*r**5 + 148*r**2 - 34*r**4 + 20*r + 1026 - 568 + 40*r**3 - 508 = 0.
-1, 1/2, 5
Let m(t) be the second derivative of -t**4/12 - 44*t**3/3 + 372*t. Determine c, given that m(c) = 0.
-88, 0
Let s = 148/17 + -3489/391. Let d = s - -107/69. Let 2*z**4 - 2/3*z**5 - d*z**3 - 2/3 - 4/3*z**2 + 2*z = 0. What is z?
-1, 1
Let b(g) be the third derivative of 0*g + 0 + 1/210*g**5 + 4/21*g**3 + 1/21*g**4 + 10*g**2. Factor b(l).
2*(l + 2)**2/7
Let 3/2*l**4 + 0*l + 3/2*l**3 + 0 - 3/2*l**2 - 3/2*l**5 = 0. Calculate l.
-1, 0, 1
Let h(m) = 5*m**2 + 21*m + 58. Let b(q) = 4*q**2 + 22*q + 60. Let u(o) = 3*b(o) - 2*h(o). Factor u(s).
2*(s + 4)*(s + 8)
Let p(u) = -2*u**3 - 8. Let x(b) = 6 + b + b**2 - 7 - b + b. Let h(z) = -p(z) + 6*x(z). Let h(g) = 0. What is g?
-1
Let o(l) be the second derivative of -l**6/210 - l**5/35 - l**4/14 - 2*l**3/21 + 9*l**2 - 2*l. Let u(m) be the first derivative of o(m). Solve u(b) = 0 for b.
-1
Suppose -2*i - 3*n = -10, 20 = 4*i - 2*n + n. Find v, given that -v**2 - 3*v**3 + v**2 + i*v**4 - 3*v**2 + v**2 = 0.
-2/5, 0, 1
Let s(g) be the second derivative of -g**6/6 + 15*g**5/4 - 35*g**4/6 + 338*g. Factor s(x).
-5*x**2*(x - 14)*(x - 1)
Let b(j) be the first derivative of -125/4*j**4 - 20*j + 15 - 75*j**3 - 60*j**2. Factor b(p).
-5*(p + 1)*(5*p + 2)**2
Let y = -2943 + 2945. What is f in -1/4*f**y + f + 0 = 0?
0, 4
Let z = 483/116 + -70/29. Find h, given that -1/4*h**3 - 5/4*h**2 - 3/4 - z*h = 0.
-3, -1
Let o(h) be the first derivative of 4*h**3/3 + 4*h**2 - 96*h - 134. Determine r, given that o(r) = 0.
-6, 4
Let r be 2295 + 1 + (-2 - 60/(-10)). Let c be (-6)/1 + r/375. Let c*t**2 - 2/15*t**3 + 0 - 2/15*t**4 + 2/15*t = 0. Calculate t.
-1, 0, 1
Factor -3/2*b**3 + 54 + 6*b - 27/2*b**2.
-3*(b - 2)*(b + 2)*(b + 9)/2
Let n(r) = 7*r**4 + 4*r**3 + 6*r**2 + 10*r + 7. Let w(o) = -20*o**4 - 12*o**3 - 18*o**2 - 29*o - 20. Let x(y) = -17*n(y) - 6*w(y). Factor x(a).
(a + 1)**4
Let p(f) be the third derivative of 6*f**2 + 0 - 1/15*f**4 + 1/150*f**5 - 1/3*f**3 + 0*f. Find y such that p(y) = 0.
-1, 5
Let x be 6272/616 - 1/11*2. Factor x - 5 - 5*b**2 + 15 + 15*b.
-5*(b - 4)*(b + 1)
Solve -8*y - 2*y + 4*y + 56*y**2 - 54*y**2 = 0 for y.
0, 3
Suppose 39 = 5*r + 2*u - 23, 3*r - 31 = 5*u. Solve -305 + r*g**3 + 305 - 8*g**2 - 4*g**5 = 0.
-2, 0, 1
Let n be (-3 - -13) + (-10)/2. Let -2*r**2 + r**3 - 4 - 13*r + n*r + r = 0. What is r?
-1, 4
Determine v so that 4*v**3 - 527 + 241*v**2 + 100 - 216*v + 22 - 37*v**2 - 11 = 0.
-52, -1, 2
Let c(d) be the first derivative of 15*d**4/4 - 665*d**3/3 - 455*d**2/2 + 225*d + 268. Factor c(t).
5*(t - 45)*(t + 1)*(3*t - 1)
Let o(r) be the first derivative of r**6/6 - r**5/5 - 9*r**4/4 + 5*r**3/3 + 8*r**2 - 12*r - 191. Factor o(m).
(m - 3)*(m - 1)**2*(m + 2)**2
Suppose 3*g - 5*k = 0, 0 = 3*g + 7*k - 2*k. Suppose -3*d = -4*c - 2, 4*c + c = 3*d - 1. Factor g + 2/9*b + 2/9*b**3 + 4/9*b**d.
2*b*(b + 1)**2/9
Suppose -16*x = -86 + 54. Factor -1/4*r**x - 1/4*r**5 + 1/4*r**4 + 1/4*r**3 + 0*r + 0.
-r**2*(r - 1)**2*(r + 1)/4
Let k(x) be the first derivative of 16*x**3/21 + 23*x**2/14 + x + 605. Factor k(h).
(h + 1)*(16*h + 7)/7
Let w = -23042 - -92169/4. Suppose -w*y**3 - 3/2 + 7/4*y + 0*y**2 = 0. Calculate y.
-3, 1, 2
Let l(k) be the first derivative of -32/3*k**3 + 0*k + 5*k**4 - 8*k**2 - 3. Factor l(y).
4*y*(y - 2)*(5*y + 2)
Let x(u) be the first derivative of 3*u**5/10 + 15*u**4/8 + 9*u**3/2 + 21*u**2/4 + 3*u - 357. Factor x(z).
3*(z + 1)**3*(z + 2)/2
Determine b so that 93*b**2 - 9*b**4 + 48*b**3 - 228*b**2 + 6*b**4 - 486*b = 0.
-2, 0, 9
Suppose -3*i + 5*i = 4. Factor -9*v**i - 12 + 14*v**2 + 12 - 25*v.
5*v*(v - 5)
Suppose -28/5 - 4/5*m**2 + 32/5*m = 0. What is m?
1, 7
Factor 1/2*g**3 + 2/3*g**4 - 2/3*g + 0 - 2/3*g**2 + 1/6*g**5.
g*(g - 1)*(g + 1)*(g + 2)**2/6
Factor -409*v**2 - 3*v**3 + 956*v**2 + 240*v - 433*v**2.
-3*v*(v - 40)*(v + 2)
Let g(f) be the second derivative of -f**6/30 + 3*f**5/20 + 3*f**4/4 + 5*f**3/6 + 32*f - 4. Factor g(w).
-w*(w - 5)*(w + 1)**2
Solve -16*x + x**5 - 4*x**5 - 27*x**4 + 69*x**4 - 24*x**2 + 47*x**3 - 46*x**5 = 0 for x.
-4/7, 0, 1
Let x be (-30318)/57 + (-4)/38. Let f = -3716/7 - x. Determine j so that 8/7*j - f + 30/7*j**2 = 0.
-2/3, 2/5
Let p(g) = 25*g - 23. Let w be p(1). Let i(q) be the third derivative of 1/540*q**6 - 1/270*q**5 + 0*q + 0*q**3 - 7*q**w + 0 + 0*q**4. Factor i(n).
2*n**2*(n - 1)/9
Suppose b - d - 4 = -0*d, 2*b + 4*d = -16. Let r(h) be the second derivative of b*h**2 + 1/12*h**4 + 0*h**3 + h + 0 + 1/20*h**5. Let r(n