9/36. Let b(w) be the first derivative of -4/3*w - 4/3*w**2 - x*w**4 - 5/9*w**3 - 10. Factor b(v).
-(v + 1)*(v + 2)**2/3
Let 8/9*v**3 + 2 - 8/3*v - 4/9*v**2 + 2/9*v**4 = 0. Calculate v.
-3, 1
Factor -52*j + 20 + 12*j - 5*j**3 + 165*j**2 - 140*j**2.
-5*(j - 2)**2*(j - 1)
Let j(a) be the first derivative of 4*a**5/5 - a**4 + 74. What is q in j(q) = 0?
0, 1
Let m(y) be the second derivative of -y**4/4 + y**3/2 + 2*y. Factor m(b).
-3*b*(b - 1)
Let g be ((221/(-459))/13)/((-4)/24). What is v in 2/9*v**4 + 0 + 2/3*v - 2/3*v**3 - g*v**2 = 0?
-1, 0, 1, 3
Let j(p) be the first derivative of 15 + 529/5*p**3 + 12/5*p - 138/5*p**2. Factor j(o).
3*(23*o - 2)**2/5
Let d(c) = -12*c + 9. Let h be d(8). Let x be (-4)/18 + h/(-27). Factor v**3 + 3*v**5 + 6*v**3 - 7*v**4 - 2*v**4 + 2*v**3 - x*v**2.
3*v**2*(v - 1)**3
Let g(u) = 6*u**5 + 622*u**4 + 16840*u**3 + 16224*u**2 + 8. Let l(r) = 2*r**5 + 207*r**4 + 5613*r**3 + 5408*r**2 + 3. Let q(w) = -3*g(w) + 8*l(w). Factor q(p).
-2*p**2*(p + 1)*(p + 52)**2
Suppose 11 - 16*m**3 + 21 + 16*m - 4*m**2 + 0*m**2 - 6*m**4 + 16*m**4 - 38 = 0. What is m?
-1, 3/5, 1
Suppose 5*v = 5*m + 165, v + 1 = -1. Let d(q) = -85*q**3 + 170*q**2 + 255*q. Let l(k) = -5*k**3 + 10*k**2 + 15*k. Let x(z) = m*l(z) + 2*d(z). Factor x(c).
5*c*(c - 3)*(c + 1)
Let w be (-4)/6*438435/270. Let z = -1081 - w. Factor 32/9*u**2 + 8/9*u + 0 + z*u**3.
2*u*(u + 2)*(7*u + 2)/9
Suppose 4*t + 10*b = 12*b - 6, 3*t = b - 3. What is z in t - 1/7*z**2 + 1/7*z**4 + 2/7*z - 2/7*z**3 = 0?
-1, 0, 1, 2
Let g(j) be the third derivative of j**6/48 - 25*j**5/48 + 85*j**4/48 - 55*j**3/24 - 353*j**2. Factor g(a).
5*(a - 11)*(a - 1)*(2*a - 1)/4
Find y such that -34/15*y**3 - 70/3*y - 2/15*y**4 - 62/5*y**2 - 196/15 = 0.
-7, -2, -1
Suppose -34 = -x - 8. Let y be (x/(-3))/((-24)/36). Factor -2 - 4*r**2 + y*r**2 + 6*r**3 + 0*r - 9*r - 4.
3*(r - 1)*(r + 2)*(2*r + 1)
Let s(n) be the first derivative of -1/6*n**3 + 1/2*n**2 + 0*n + 2. Suppose s(j) = 0. Calculate j.
0, 2
Let a(p) be the second derivative of -5*p**7/42 - p**6/2 + p**5/2 + 5*p**4 + 20*p**3/3 - 5*p + 1. Determine f, given that a(f) = 0.
-2, -1, 0, 2
Let p = 14 + -11. Suppose 0*g + p*g = 12. Factor -5*a**2 - 7*a**2 - a + a**5 + 14*a**2 - 2*a**g.
a*(a - 1)**3*(a + 1)
Let q = 226 + -108. Factor q*n - 40*n**2 + 2*n**3 - 5*n**5 - 83*n + 10*n**4 + 8*n**3 - 10.
-5*(n - 1)**4*(n + 2)
Let y = 196 - 325. Let c = y - -907/7. Find q such that 0*q - c*q**3 + 18/7*q**4 + 0*q**2 + 0 - 2*q**5 = 0.
0, 2/7, 1
Let s(p) be the third derivative of -31*p**6/12 + 119*p**5/15 + 35*p**4/3 + 8*p**3/3 + 118*p**2. Let s(c) = 0. Calculate c.
-2/5, -2/31, 2
Suppose -18 = -18*q + 18. Let m(r) be the first derivative of 0*r**q + 4 + 0*r + 2/39*r**3. Factor m(i).
2*i**2/13
Determine s, given that 27 - 7883*s**4 + 13*s**2 + 10*s**3 + 7884*s**4 + 9 - 60*s = 0.
-6, 1
Let t(c) be the first derivative of c**8/504 + c**7/1260 - 4*c**2 - 12. Let g(b) be the second derivative of t(b). Factor g(u).
u**4*(4*u + 1)/6
Suppose y + v + 2 = 0, -3*v = 2*y + 2*y + 6. Let z(t) be the first derivative of 1/8*t**2 - 5 + 1/16*t**4 + 1/6*t**3 + y*t. Let z(j) = 0. What is j?
-1, 0
Let u be (-250)/100 + (0 - (-12)/(1 + 3)). Determine o, given that 1/6 - 1/6*o**5 + 1/2*o - u*o**4 + 1/3*o**2 - 1/3*o**3 = 0.
-1, 1
Let j(h) be the first derivative of 2/3*h**3 - 8 + 0*h**2 - h + 0*h**4 - 1/5*h**5. Determine k so that j(k) = 0.
-1, 1
Let z(v) be the second derivative of v**5/70 - v**4/84 - 11*v**3/42 + 5*v**2/7 + 141*v. Let z(u) = 0. Calculate u.
-5/2, 1, 2
Let n be 4/(-6)*(-129)/215. Suppose -5*g + 2*y = 6, -5 = -3*g - 4*y + 7. Factor -2/5*c**2 + g - n*c.
-2*c*(c + 1)/5
Let v(q) be the first derivative of -6 + 0*q**2 - 1/20*q**5 + 0*q**4 + 1/12*q**3 + 0*q. Factor v(s).
-s**2*(s - 1)*(s + 1)/4
Let r = 124 + -146. Let z be 1 - -2 - 7 - r/4. Factor 6 - z*t**3 + 0*t - 9/2*t**2.
-3*(t - 1)*(t + 2)**2/2
Suppose -3*d = -5*r + 13, 3*r + 3*d - 14 - 13 = 0. Suppose 37*b**r + 6*b**3 + 3*b**3 + 20*b**4 - 5*b**3 - 61*b**5 = 0. Calculate b.
-1/6, 0, 1
Let i = -1754 + 1754. Solve -2/3*z**2 + i + 0*z - 1/3*z**5 - 5/3*z**3 - 4/3*z**4 = 0 for z.
-2, -1, 0
Let q = -6503 + 6503. What is g in q*g - 6/7*g**2 + 0 - 1/7*g**3 = 0?
-6, 0
Let c be 6*(-2 - (-28)/12). Let f(d) be the first derivative of -4*d**2 - d**2 + 11*d + c - d**2 + d**3 + d. Factor f(x).
3*(x - 2)**2
Suppose 0 = s + 2*c + 7, s + 5 = -2*c + c. Let i be 135/30 - s/(-2). Factor -1/2*o**i + 1/2*o - 1/2 + 1/2*o**2.
-(o - 1)**2*(o + 1)/2
Factor -52/7*o**2 + 88/7*o + 4/7*o**4 - 40/7*o**3 + 0.
4*o*(o - 11)*(o - 1)*(o + 2)/7
Let c(d) = -7*d - 3. Let j be c(-3). Determine m so that j*m + 12 - 6*m**2 + 7*m + m - 5*m = 0.
-1/2, 4
Let z(h) be the first derivative of -h**9/9072 - h**8/5040 + 28*h**3/3 - 44. Let i(d) be the third derivative of z(d). Factor i(b).
-b**4*(b + 1)/3
Let u = 76 - 74. Find y such that 3*y - 3*y**2 + 2*y**2 - 4*y**u - 2 + 4*y**2 = 0.
1, 2
Suppose -69 = -3*u - 3*n, -2*u + 2*n + 16 = -18. Suppose -2*g + 10 = 4*v - 0, -u = v + 5*g. Determine y so that 9*y + 0*y + v - 19*y - 15*y**2 = 0.
-1, 1/3
Suppose 2*y = 19*y + 12*y. Let h(g) be the third derivative of 0*g**5 + 1/120*g**6 + 0*g**4 + y*g - 3*g**2 + 0*g**3 + 0. Factor h(j).
j**3
Factor -21*l - 18*l - 6*l**2 + 40 - 6*l + 10*l**2 + l**2.
5*(l - 8)*(l - 1)
Let m(n) be the first derivative of -3*n**5/5 + 9*n**3 - 6*n**2 - 36*n + 54. Find x, given that m(x) = 0.
-3, -1, 2
Let r(o) = o**3 - 9*o**2 + o - 8. Let d be r(9). Let c be d + 4/(-8 - -4). Suppose 0 + p**4 - 1/2*p**3 + c*p**2 + 0*p - 1/2*p**5 = 0. Calculate p.
0, 1
Let j = 21 - 15. Suppose p = 4*r - 21, -3*r + j*r - 7 = -p. Let -6*k**3 - 2*k**2 + 160*k**4 - 159*k**r + 11*k**2 = 0. What is k?
0, 3
Let c be ((-4)/18)/((-24)/36). Let a(u) be the third derivative of 0*u + 3/8*u**4 - 1/5*u**5 + 6*u**2 + 0 + 1/30*u**6 - c*u**3. Determine k so that a(k) = 0.
1/2, 2
Factor 131*g + 10700 + 6705 + 5*g**2 + 11*g - 732*g.
5*(g - 59)**2
Let f(a) be the first derivative of -a**5/150 + 2*a**4/15 - 16*a**3/15 - 8*a**2 + 9. Let z(p) be the second derivative of f(p). Factor z(m).
-2*(m - 4)**2/5
Suppose -4*g = 2*f - 30, f = -0*g + g. Let y be (f/((-50)/(-12)))/(4 + -2). What is p in -12/5 - y*p**5 + 21/5*p**2 + 0*p - 9/5*p**4 + 3/5*p**3 = 0?
-2, -1, 1
Let d(j) be the first derivative of -2*j**6/3 - 28*j**5/5 + 82*j**4 - 848*j**3/3 + 336*j**2 - 575. Determine n so that d(n) = 0.
-14, 0, 2, 3
Let f = 294 + -290. Suppose -c - 3 = -5*c - 3*r, 0 = 3*c + 4*r - f. Factor c + 0*v - 5/3*v**2.
-5*v**2/3
Let a(b) be the third derivative of -13*b**8/168 - 2*b**7/105 + 169*b**6/60 + 91*b**5/15 + 2*b**4 + 46*b**2 - b. Solve a(d) = 0 for d.
-3, -1, -2/13, 0, 4
Let l(m) be the first derivative of 2*m**3/3 - 36*m**2 + 198*m - 467. Factor l(q).
2*(q - 33)*(q - 3)
Let k(z) = -z**4 - 11*z**3 - 32*z**2 + 179*z + 198. Let v(j) = 6*j**4 + 67*j**3 + 191*j**2 - 1073*j - 1186. Let t(i) = 34*k(i) + 6*v(i). Factor t(f).
2*(f - 3)*(f + 1)*(f + 8)**2
Let z(m) be the second derivative of -m**6/24 - m**5/6 + 7*m**2/2 + 6*m. Let l(a) be the first derivative of z(a). Let l(k) = 0. Calculate k.
-2, 0
Suppose 24*z + 56 = 4*q + 20*z, 0 = -2*q + z + 32. Let k be (q/45)/((-39)/(-15) - 1). Find j such that 0*j**2 + 1/8*j**5 + 1/8*j**3 + 0 + 0*j - k*j**4 = 0.
0, 1
Let l(d) = -4*d**2 + 33*d - 32. Let g be l(7). Factor -h**g - 1/2*h**4 - 1/2 + h**2 + 1/2*h**5 + 1/2*h.
(h - 1)**3*(h + 1)**2/2
Let w(u) be the first derivative of -2*u**3/21 - 23*u**2/7 - 44*u/7 + 100. Factor w(s).
-2*(s + 1)*(s + 22)/7
What is z in 7*z**2 - 4*z + 32*z - 6*z**2 + 24*z = 0?
-52, 0
Let u(n) be the second derivative of -n**4/60 - 5*n**3/6 - n - 10. What is m in u(m) = 0?
-25, 0
Let h(b) be the first derivative of -1 - 1/4*b**4 + 4/9*b**3 - 2/3*b + 5/6*b**2. Factor h(d).
-(d - 2)*(d + 1)*(3*d - 1)/3
Let g(i) = -i**2 + 2*i + 6. Let f be g(3). Let t be 0 + 0/(-4 - (-6 + f)). Suppose -1/4*l**5 + 3/4*l**4 + 0*l - 3/4*l**3 + 1/4*l**2 + t = 0. What is l?
0, 1
Let b = 46 + -46. Suppose b = -2*v + 2*a - 4*a + 14, v = 2*a - 8. Factor -3/4*g**3 + 1/4*g**4 + 0 + 3/4*g**v - 1/4*g.
g*(g - 1)**3/4
Let i(k) be the third derivative of k**8/336 - 11*k**7/42 + 97*k**6/12 - 475*k**5/6 - 12635*k**4/24 - 6859*k**3/6 + 287*k**2. Factor i(n).
(n - 19)**3*(n + 1)**2
Let q(b) be the third derivative of 0*b**3 - b**2 - 1/336*b**8 