*2 + 3*u + 0 = 0.
0, 6
Let j be (-10)/25 - 289/15. Let o = -58/3 - j. Factor -o*z**4 + z + 5/3*z**2 + 1/3*z**3 + 0.
-z*(z - 3)*(z + 1)**2/3
Let a be 4 + (2 + 0)*-4. Let c(s) = -8*s**2 - 13*s - 9. Let d(j) = -j**2 - j - 1. Let i(p) = a*c(p) + 36*d(p). Factor i(n).
-4*n*(n - 4)
Let j = -1/18 - -2/9. Let y = -425/2 + 213. Factor y*l - j*l**2 - 1/3.
-(l - 2)*(l - 1)/6
Let i(k) be the second derivative of 5*k**4/12 + 20*k**3/3 + 75*k**2/2 - 9*k - 2. Factor i(z).
5*(z + 3)*(z + 5)
Let m = -85/14 + 15/2. Let n be ((-132)/(-56))/11*(15 + -15 + 4). Factor 2/7*l + 0 + n*l**4 - m*l**3 + 2/7*l**2.
2*l*(l - 1)**2*(3*l + 1)/7
Factor 4/7*o - 2/7*o**2 - 2/7*o**3 + 0.
-2*o*(o - 1)*(o + 2)/7
Let k(d) = -d**2 + 8*d + 14. Let o be k(10). Let a be (-18)/12 - (-2 + (-1)/o). Factor a*x**2 - 2/3 - 1/3*x.
(x - 2)*(x + 1)/3
Let h(x) be the third derivative of -x**7/630 - 2*x**6/45 - 53*x**5/180 - 31*x**4/36 - 4*x**3/3 + 185*x**2. Factor h(f).
-(f + 1)**2*(f + 2)*(f + 12)/3
Let q(n) be the first derivative of -9*n**4/20 + n**3 + 6*n**2/5 - 12*n/5 - 38. Factor q(l).
-3*(l - 2)*(l + 1)*(3*l - 2)/5
Let o(c) = -3*c**2. Let p(l) = 11*l**2 - 22*l + 23. Let d(v) = -20*o(v) - 5*p(v). Determine q, given that d(q) = 0.
-23, 1
Suppose 5*k = 2*k + 4*k. Let w = 0 + k. Factor 0*o + w - 2/9*o**2.
-2*o**2/9
Let f(r) be the third derivative of r**9/1350 - r**8/252 + 37*r**7/4200 - r**6/100 + 11*r**5/60 - 8*r**2. Let y(d) be the third derivative of f(d). Factor y(a).
2*(4*a - 3)**2*(7*a - 2)/5
Let x be (2 + -3)/(5/(-30)). Let k(w) = -2*w**2 - 12*w - 18. Let y(q) = 4*q**2 + 24*q + 36. Let g(t) = x*y(t) + 11*k(t). Factor g(s).
2*(s + 3)**2
Determine m so that 3/2*m**2 + 816*m + 110976 = 0.
-272
Let o(g) be the first derivative of -21/2*g**2 + 5 - 18*g**5 + 129/4*g**4 + 6*g - 8*g**3. What is f in o(f) = 0?
-2/5, 1/3, 1/2, 1
Factor -6*u**3 - 40/3*u**2 - 26/3*u - 4/3.
-2*(u + 1)**2*(9*u + 2)/3
Let h be (4/(-6))/((-16)/54*3). Let 3/2*z - h*z**2 - 3/4 = 0. Calculate z.
1
Let x(p) be the first derivative of 2*p**6/3 + 8*p**5/5 + p**4 - 33. Find b, given that x(b) = 0.
-1, 0
Factor -25*q**2 - 32*q - 9*q**2 + 23*q**3 - 25*q**3.
-2*q*(q + 1)*(q + 16)
Let i(x) be the first derivative of -x**8/12600 + x**7/6300 + x**6/1350 - 5*x**3/3 + 2. Let a(y) be the third derivative of i(y). Factor a(n).
-2*n**2*(n - 2)*(n + 1)/15
Let 0 + 0*j + 7/4*j**3 + 3/2*j**2 + 1/4*j**4 = 0. Calculate j.
-6, -1, 0
Let n(o) be the third derivative of o**5/20 + o**4/4 - 4*o**3 + o**2 - 2*o. Factor n(j).
3*(j - 2)*(j + 4)
Determine f so that 3*f**4 - 68 + 10*f**2 + 17*f**2 - 15*f**3 + 74 - 6*f - 15*f = 0.
1, 2
Let o = -1183/9 - -1213/9. Factor -o*z**2 + 4/3 + 2*z.
-2*(z - 1)*(5*z + 2)/3
Let i(m) be the third derivative of -m**9/4032 - m**8/2240 - 7*m**3/3 + 4*m**2. Let d(u) be the first derivative of i(u). Factor d(f).
-3*f**4*(f + 1)/4
Let o(h) be the first derivative of h**6/3 + 3*h**5/10 - 7*h**4/6 - h**3 + 2*h**2 - 30*h + 26. Let k(s) be the first derivative of o(s). Factor k(c).
2*(c - 1)*(c + 1)**2*(5*c - 2)
Let z = 6119/1916 + 27/479. Factor 11/4*o**2 + 1/2 + z*o.
(o + 1)*(11*o + 2)/4
Let b(a) = a**3 + 7*a**2 + 4*a + 2. Let o be b(-6). Factor -8*u**4 + 8*u**5 - 4*u**5 + o*u**2 - 4*u - 6*u**2.
4*u*(u - 1)**3*(u + 1)
Let r be 7/21 - 147/9. Let z be 4/6*4/r*-8. Let -z*m + m**3 + 0*m**2 + 0 + 1/3*m**4 = 0. Calculate m.
-2, 0, 1
Factor 34/5*z + 32/5 + 2/5*z**2.
2*(z + 1)*(z + 16)/5
Suppose 2*o - 7*s - 28 = -12*s, -2*s = 2*o - 16. Let a be (-6)/o*-4*(-2)/(-15). Let a*t**2 + 0 - 4/5*t**3 + 0*t = 0. What is t?
0, 1
Let b = 116 + -125. Let z be 0 + 1 - (-7)/b. What is s in 8/9*s - 2/9*s**4 + 4/3*s**2 - 16/9 - z*s**3 = 0?
-2, 1, 2
Let g(y) be the first derivative of 3*y**5/5 + 63*y**4/4 - y**3 - 63*y**2/2 + 5. Factor g(m).
3*m*(m - 1)*(m + 1)*(m + 21)
Let o(v) be the first derivative of 5*v**4 + 632*v**3/3 + 2432*v**2 - 2048*v + 86. Factor o(h).
4*(h + 16)**2*(5*h - 2)
Let b = -29181 + 29184. Factor 1/4*n + 0 + 3/4*n**b - 3/4*n**2 - 1/4*n**4.
-n*(n - 1)**3/4
Let l = -21 + 24. Suppose 0 + 12 = l*t. Factor -t*g**3 + 2*g**3 + 20*g**2 - 8*g - 6*g**3.
-4*g*(g - 2)*(2*g - 1)
Let z(p) be the first derivative of -p**4/2 - 5*p**3/6 + 7*p**2/4 + p + 86. Suppose z(a) = 0. What is a?
-2, -1/4, 1
Let -16/7*f + 0 + 20/7*f**2 + 6/7*f**3 - 8/7*f**4 - 2/7*f**5 = 0. Calculate f.
-4, -2, 0, 1
Let -12/5*o + 2/5*o**2 - 14/5 = 0. What is o?
-1, 7
Let p = 13 + -10. Suppose p*r = 2*o - o + 16, 3*r = 3*o + 24. Find j, given that 12*j**3 - 99*j**r + 39*j**4 - 2*j**5 + 77*j**5 = 0.
0, 2/5
Let w(h) be the first derivative of h**6/24 - h**5/20 - h**4/8 - 488. Factor w(o).
o**3*(o - 2)*(o + 1)/4
Let l(z) = 2*z + 13. Let s be l(11). Let y = s - 24. Factor -5*n**2 - y*n**2 + 7*n - 8 + n + 14*n**2.
-2*(n - 2)**2
Let o(g) be the third derivative of -16*g**7/525 - 2*g**6/15 + 31*g**5/150 + 11*g**4/30 + g**3/5 - 5*g**2 - 12*g. Solve o(a) = 0.
-3, -1/4, 1
Suppose -22/7*i**3 + 0 + 22/7*i - 2/7*i**2 + 2/7*i**4 = 0. Calculate i.
-1, 0, 1, 11
Determine p so that -2/13*p**3 + 0 - 8/13*p**2 + 8/13*p + 2/13*p**4 = 0.
-2, 0, 1, 2
Suppose -2*q + 0*q = -6. Factor -3 - 4*c - q*c**2 + 4*c**2 + 3*c - c.
(c - 3)*(c + 1)
Let p = 49 + -46. Factor -2*v**p - 2*v + 2*v + 20*v**2 - 24*v**2.
-2*v**2*(v + 2)
Let d(p) be the third derivative of p**5/120 - 31*p**4/48 - 11*p**3/2 - 19*p**2 + 5. Factor d(j).
(j - 33)*(j + 2)/2
What is n in -1/2*n**4 - 40*n**2 + 0 - 32*n - 17/2*n**3 = 0?
-8, -1, 0
Suppose -118*k = 49*k - 334. Factor u**3 - u - 3/2 - 1/2*u**4 + k*u**2.
-(u - 3)*(u - 1)*(u + 1)**2/2
Suppose -6*m + 4*m = -6. Suppose -5*t + m*y = -136, 5*t = 2*t + 2*y + 82. Factor -10*g**3 + 16*g**2 - 26 + t - 8*g + 2*g**4.
2*g*(g - 2)**2*(g - 1)
Let y(m) be the second derivative of -m**4/6 - 13*m**3/3 - 12*m**2 - 101*m. Factor y(i).
-2*(i + 1)*(i + 12)
Suppose -40/7*r**2 + 48/7*r + 2/7*r**4 + 4/7*r**3 + 0 = 0. What is r?
-6, 0, 2
Let d(h) be the first derivative of 2*h**3/3 + 24*h**2 - 50*h + 11. Factor d(c).
2*(c - 1)*(c + 25)
Let o be (-515)/9975 + 6/9. Let k = o - 2/133. Let -6/5 + 3/5*i + k*i**2 = 0. What is i?
-2, 1
Let a(n) be the third derivative of n**6/105 + 17*n**5/210 - 4*n**4/21 - 5*n**3/21 + 553*n**2. Suppose a(m) = 0. Calculate m.
-5, -1/4, 1
Solve 4*l**4 - 16912 - 26*l**2 + 8456 - l**5 + 8424 + 11*l**3 - 64*l = 0 for l.
-2, -1, 4
Let n(x) = -x**2 + 7*x - 2. Let g be n(6). Suppose 268*y + 2*y**g - 268*y + 2*y**5 = 0. Calculate y.
-1, 0
Factor -2/19*v**3 + 0 + 6/19*v**2 + 8/19*v.
-2*v*(v - 4)*(v + 1)/19
Let c(u) = -u**2 + u. Let g(a) be the third derivative of -2*a**5/15 + 17*a**4/24 - 25*a**3/6 - 4*a**2. Let f(q) = 28*c(q) - 4*g(q). Factor f(k).
4*(k - 5)**2
Let d = 984223/5 + -198904. Let t = -2053 - d. Let 12/5*s + t*s**2 + 0 - 12/5*s**3 = 0. What is s?
-1/3, 0, 3
Let g(h) be the second derivative of 16/3*h**3 + 32*h**2 + 1/5*h**5 + 0 - 7/3*h**4 + 17*h. Factor g(p).
4*(p - 4)**2*(p + 1)
Let c(j) = -3*j - 39. Let q be c(-13). Let u(o) be the third derivative of -1/60*o**5 + q*o + 6*o**2 + 1/8*o**4 + 0 - 1/3*o**3. Factor u(r).
-(r - 2)*(r - 1)
Let p(u) = 8*u**3 - 190*u**2 - 8*u + 199. Let r(o) = 9*o**3 - 190*o**2 - 9*o + 202. Let w(s) = 4*p(s) - 3*r(s). Let w(z) = 0. What is z?
-1, 1, 38
Factor 32/5*a - 18/5*a**2 + 8/5.
-2*(a - 2)*(9*a + 2)/5
Suppose -3*h + 16 + 8 = 0. Let z(s) = 4*s - 32. Let w be z(h). Find r, given that -4/5*r + 0 + w*r**3 + 6/5*r**2 - 2/5*r**4 = 0.
-2, 0, 1
Let p(k) be the first derivative of -10/3*k + 25 - 14/9*k**3 + 1/3*k**4 - 14/3*k**2. Factor p(u).
2*(u - 5)*(u + 1)*(2*u + 1)/3
Let s = -34326/77 + 4910/11. Factor -s*c**2 + 24/7*c - 32/7.
-4*(c - 4)*(c - 2)/7
Let n = 78 - 77. Let g be (-8 + 4 - -8) + (n - 3). Find w such that 1/2*w + 0 + 1/2*w**g = 0.
-1, 0
Let w(b) = 7*b**5 - 17*b**4 + 39*b**3 - 28*b**2 + 11*b - 3. Let k = -18 + 19. Let a(o) = -o**5 - o**4 - o**3 - o + 1. Let c(h) = k*w(h) + 3*a(h). Factor c(q).
4*q*(q - 2)*(q - 1)**3
Let x = 81 + -79. Suppose -4 = 3*d - 2*t, 0 = -x*t + 1 + 9. Factor 72/7*n**d - 24/7*n + 2/7.
2*(6*n - 1)**2/7
Let y(t) = 3*t**5 + t**4 + t + 3. Let h(o) = -16*o**5 - 5*o**4 - o**3 - o**2 - 5*o - 16. Let b(v) = 2*h(v) + 11*y(v). Factor b(p).
(p - 1)**2*(p + 1)**3
Suppose 7*o**2 - 23*o**3 + 2*o**3 + 6*o**2 - 2*o = 0. Calculate o.
0, 2/7, 1/3
Suppose 432 + 3/2*g**3 + 39*g**2 + 288*g = 0. Calculate g.
-12, -2
Suppose -t - t 