(v - 3)*(v - 2)
Let s(q) be the third derivative of -1/480*q**6 - 122*q**2 + 1/4*q**3 + 1/40*q**5 + 0*q - 11/96*q**4 + 0. Factor s(c).
-(c - 3)*(c - 2)*(c - 1)/4
Suppose -53*u + 0 - 1/4*u**2 = 0. What is u?
-212, 0
Let o(n) = 2*n - 13. Let z be o(7). Let s be 12 + (-1 + -3)/z. Determine k, given that -s*k - 5*k**2 + 2 - 2 + 3*k = 0.
-1, 0
Let h = -4340 - -4340. Let l(j) be the second derivative of 1/7*j**3 - 1/42*j**4 - 2/7*j**2 - 22*j + h. Factor l(d).
-2*(d - 2)*(d - 1)/7
Let d be 36512/(-5216)*(0 - (-12)/(-14)). Find z, given that 3/4*z**4 - 3/4*z**2 + 0 + 6*z**3 - d*z = 0.
-8, -1, 0, 1
Let k be (20 - 4) + 1410/(-90). Let r(p) be the first derivative of 10 + p + k*p**2 - 1/9*p**3. Factor r(y).
-(y - 3)*(y + 1)/3
Let o(c) be the first derivative of -3*c**5/5 - 33*c**4/4 + 72*c**3 - 186*c**2 + 192*c - 1461. Determine x, given that o(x) = 0.
-16, 1, 2
Let v(b) be the first derivative of -3*b**4/4 + 13*b**3/3 + 14*b**2 + 12*b + 1175. Let v(x) = 0. What is x?
-1, -2/3, 6
Factor -48/7 - 18/7*s**2 + 52/7*s + 2/7*s**3.
2*(s - 4)*(s - 3)*(s - 2)/7
Factor 25*n - 154/3 + 1/3*n**2.
(n - 2)*(n + 77)/3
What is n in 2*n**3 + 37/2*n**2 + 44*n + 30 = 0?
-6, -2, -5/4
Let i be 3689/204 + -21 - ((-2 - 0) + -1). Let q(a) be the third derivative of 0*a - 1/6*a**3 + 0 + 13*a**2 - i*a**4 - 1/60*a**5. Factor q(g).
-(g + 1)**2
Let u(n) be the first derivative of 22*n**3/27 - 337*n**2/9 - 248*n/9 + 2561. Factor u(j).
2*(j - 31)*(11*j + 4)/9
Let r = 22 + -19. Suppose -r*q = -6*q + 9. Find w such that 0*w - 7*w + 56*w**2 - 12*w**q - 21*w - 16 = 0.
-1/3, 1, 4
Let t(r) = -35*r**3 - 3865*r**2 - 96350*r - 698955. Let p(b) = 5*b**3 + 552*b**2 + 13764*b + 99850. Let g(y) = 15*p(y) + 2*t(y). Determine x so that g(x) = 0.
-78, -16
Let o(y) be the first derivative of 0*y - 10/3*y**3 - 99 + 5/6*y**6 + 0*y**2 + 2*y**5 - 5/4*y**4. Factor o(a).
5*a**2*(a - 1)*(a + 1)*(a + 2)
Suppose 20 - 15 = f. Suppose 0 = -x - f*x + 30. Suppose -5 + 10*k**x - 10*k**3 + 0*k**3 - 18*k**4 + 22*k**2 + 3*k**4 - 2*k**2 = 0. Calculate k.
-1, -1/2, 1
Let d(f) = -f**3 + 6*f**2 - f + 1. Let l(n) = -18*n**3 - 264*n**2 + 106*n - 2. Let t(w) = -2*d(w) - l(w). Factor t(v).
4*v*(v + 13)*(5*v - 2)
Let t(j) be the third derivative of -j**7/21 - 5*j**6/24 + 143*j**5/12 - 175*j**4/12 + 3371*j**2. Determine w so that t(w) = 0.
-10, 0, 1/2, 7
Let i(z) be the third derivative of -z**7/210 + 5*z**6/8 - 49*z**5/20 + 73*z**4/24 - 14*z**2 - 118. Solve i(s) = 0.
0, 1, 73
Let x(m) be the second derivative of -m**6/14 - 204*m**5/35 + 447*m**4/28 - 29*m**3/7 - 24*m**2 + m + 2520. What is g in x(g) = 0?
-56, -2/5, 1
Let r(q) = 2*q**2 + 30*q - 13. Let p(a) = -a**2 - 27*a + 14. Suppose 3*i = -2*g - 11, 0*g - 3*g = -2*i - 16. Let f(v) = i*p(v) - 4*r(v). Factor f(d).
-3*(d - 3)*(d - 2)
Factor -120 + 2*x**3 + 26*x**2 - 801*x + 72 + 821*x.
2*(x - 1)*(x + 2)*(x + 12)
What is b in 5*b**4 + 0 + 58*b**2 - 1/2*b**5 + 30*b + 67/2*b**3 = 0?
-2, -1, 0, 15
Let z = 105800 - 105798. Let 1/2*v**z + 0 + 11/2*v = 0. What is v?
-11, 0
Let -44/3*y**4 + 10/3*y**5 + 0 + 128/3*y**2 - 40/3*y - 18*y**3 = 0. Calculate y.
-2, 0, 2/5, 1, 5
Let x(c) = 4*c**2 - 60*c + 98. Let g(f) be the third derivative of -f**5/15 + 31*f**4/12 - 33*f**3/2 - 11*f**2 + 2. Let s(v) = -2*g(v) - 3*x(v). Factor s(b).
-4*(b - 12)*(b - 2)
Let c(l) be the second derivative of -2*l**7/21 + 2*l**6/21 + 2*l**5/35 + 6*l + 43. Factor c(d).
-4*d**3*(d - 1)*(7*d + 2)/7
Let f(x) be the first derivative of 2*x**3/27 + 100*x**2/3 + 598*x/9 - 4603. Factor f(l).
2*(l + 1)*(l + 299)/9
Let z(g) = 3*g**4 + 72*g**3 + 135*g**2 + 12*g + 6. Let q(n) = 3*n**4 + 75*n**3 + 135*n**2 + 14*n + 7. Let m(f) = 6*q(f) - 7*z(f). Factor m(c).
-3*c**2*(c + 3)*(c + 15)
Suppose 5*d + 6 - 24 = -4*s, 8 = 3*s + d. Let f = 3551/14140 - 4/3535. Let 1/4*l**4 + 1/2 - 3/4*l**s - 1/4*l**3 + f*l = 0. Calculate l.
-1, 1, 2
Let v = -101179/10 - -10118. Let x(w) be the second derivative of v*w**5 + 0*w**2 + 0 + 0*w**3 + 1/15*w**4 + 36*w. Factor x(t).
2*t**2*(5*t + 2)/5
Let p(j) be the second derivative of j**5/210 + 2*j**4/7 + 3*j**3 + 90*j**2/7 + 9342*j. Factor p(t).
2*(t + 3)**2*(t + 30)/21
Suppose 5*v + 3*i + 1325 = 8*i, 0 = -3*i + 12. Let c = v - -266. Suppose 0*x**2 + 0*x**4 + 0 + 1/2*x**c + 1/2*x - x**3 = 0. What is x?
-1, 0, 1
Factor 486 + i**2 + 2*i**2 + 119*i + 115*i + 15*i.
3*(i + 2)*(i + 81)
Suppose 37 - 10 = 3*a. Suppose 0 = 5*f - a*f + 12. Determine g, given that -5*g + 15*g**3 + 12*g + 24*g**2 + f*g**4 + 5*g = 0.
-2, -1, 0
Factor 50112/5*r + 363312*r**2 + 35364050*r**4 + 5853360*r**3 + 2592/25.
2*(145*r + 6)**4/25
Let a = 1025 + -1055. Let r be -5*(27/a - 1/(-2)). Factor 12*z + 3 - 195/4*z**r.
-3*(5*z - 2)*(13*z + 2)/4
Find i, given that -244/15*i + 112/5 - 2/15*i**4 + 14/15*i**2 + 16/15*i**3 = 0.
-4, 2, 3, 7
Let n(m) be the third derivative of m**5/12 - 185*m**4/12 + 6845*m**3/6 + 2*m**2 + m - 12. Find u, given that n(u) = 0.
37
Let x = -5495/9 + 611. Let c(p) be the second derivative of -x*p**2 + 0 + 1/3*p**3 + 15*p - 1/9*p**4 + 1/90*p**5. Find f, given that c(f) = 0.
1, 4
Let h = -882 + 1140. Suppose h = -13*b + 323. Let 44/5*s**2 + 14/5*s**4 + 36/5*s**3 + 26/5*s + 2/5*s**b + 6/5 = 0. What is s?
-3, -1
Factor -1584 - 1554*x**3 + 511*x**3 - 408*x**2 - 1596*x + 517*x**3 + 523*x**3.
-3*(x + 2)**2*(x + 132)
Factor -d**4 + 3*d**2 - 4*d + 2*d**4 + 2*d**3 - 4185 - 2*d**4 + 4181 + 0*d**3.
-(d - 2)**2*(d + 1)**2
Let a(b) = 35*b**2 + 116*b - 121. Let h(c) = -46*c**2 - 116*c + 122. Let s(d) = 4*a(d) + 3*h(d). Determine k, given that s(k) = 0.
-59, 1
Let v(c) be the third derivative of c**8/1680 + 17*c**7/630 + 4*c**6/9 + 32*c**5/15 - c**4 + 8*c**2. Let j(n) be the second derivative of v(n). Factor j(y).
4*(y + 1)*(y + 8)**2
Suppose -3/7*i - 3/7*i**5 + 6/7*i**3 - 24/7*i**2 + 12/7*i**4 + 12/7 = 0. What is i?
-1, 1, 4
Let v be ((-3)/2)/(-12*(-6)/(-480)). Suppose 0 = v*t + 185 - 205. Factor -4/9*n + 0 - 2*n**t.
-2*n*(9*n + 2)/9
Let j(i) be the first derivative of 1/270*i**5 + 16/27*i**3 + 2/27*i**4 + 0*i - 13 + 5/2*i**2. Let y(d) be the second derivative of j(d). Factor y(u).
2*(u + 4)**2/9
Suppose -5*s = -5, -5*z + 3 = 5*s - 12. What is c in 10*c**2 - 2*c**3 - 21*c + 7*c + 6*c**z = 0?
0, 1, 7
Let b(r) = r**2 + 58*r + 71. Let l(v) = -2*v**2 + v - 4. Let h(d) = -b(d) - 2*l(d). Suppose h(n) = 0. Calculate n.
-1, 21
Suppose -21883 = 42*p - 22009. Let -4/5*l**2 + 2/5*l**4 + 6/5*l**p - 24/5*l - 16/5 = 0. Calculate l.
-2, -1, 2
Let z be (50/(-8))/((-70)/336). Let d be (-185)/z*-3 - (3 + 3). Factor 15 + 5/2*k**3 - 5*k**2 - d*k.
5*(k - 3)*(k - 1)*(k + 2)/2
Let t = -2680 + 128647/48. Let x(k) be the third derivative of 0 + 16/105*k**7 + 0*k - 3/10*k**5 + t*k**4 + 1/6*k**3 - 7/15*k**6 - 9*k**2. Solve x(z) = 0.
-1/4, 1/4, 2
Let z(v) be the second derivative of -v**6/90 - v**5/60 + v**4/9 + 2*v**3/9 - 533*v. Solve z(g) = 0 for g.
-2, -1, 0, 2
Let a(r) be the second derivative of r**6/75 - 13*r**5/50 + 13*r**4/15 + 112*r**3/15 - 1054*r. Factor a(g).
2*g*(g - 8)*(g - 7)*(g + 2)/5
Let v(r) = 3*r**2 + 6807*r + 13503. Let b(s) = -5*s**2 - 11912*s - 23628. Let f(d) = 9*b(d) + 16*v(d). Factor f(k).
3*(k + 2)*(k + 566)
Let m be 8/(-710)*20/24. Let o = m - -2570/1491. Factor 0 - o*x - 6/7*x**3 - 18/7*x**2.
-6*x*(x + 1)*(x + 2)/7
Factor -1337*p + 5*p**2 + 76860 + 130996 + 201124 - 1384*p - 139*p.
5*(p - 286)**2
Let 169*c**2 + 212*c**2 - 1261*c**2 - 15*c**3 + 1350 - 3755*c = 0. What is c?
-54, -5, 1/3
Let k(p) be the second derivative of -p**5/5 + 206*p**4/3 - 821*p**3/6 + 205*p**2/2 + 3932*p. Factor k(f).
-(f - 205)*(2*f - 1)**2
Solve -18/7*m**2 - 58/7*m + 76/7 = 0 for m.
-38/9, 1
Let v(r) = -2*r - 50. Let g be v(-26). Factor -4 - g - 2 - 3*j**2 - 9*j + 2.
-3*(j + 1)*(j + 2)
Let l(d) be the first derivative of -2*d**5/5 + 65*d**4/8 - 166*d**3/3 + 559*d**2/4 - 60*d + 3987. Find y such that l(y) = 0.
1/4, 3, 5, 8
Let i(m) be the second derivative of m**5/360 + 5*m**4/144 - 2*m**3/3 - 64*m**2 - 16*m + 1. Let h(o) be the first derivative of i(o). Find d such that h(d) = 0.
-8, 3
Let k(a) = 43639*a + 2. Let z be k(0). Factor 4*m + 14/3 - 2/3*m**z.
-2*(m - 7)*(m + 1)/3
Let i(r) be the third derivative of -r**8/112 + 3*r**7/35 + 9*r**6/40 - 5*r**5/2 - 9*r**4/2 + 36*r**3 + 2587*r**2. Solve i(t) = 0 for t.
-2, 1, 3, 6
Let c(u) = -u**3 + 25*u**2 - 2*u 