f(r) be the first derivative of -20/3*r**3 + 0*r - 1 + 2*r**4 - m*r**2 + 4*r**5. Factor f(x).
4*x*(x - 1)*(x + 1)*(5*x + 2)
Let b(y) = 4*y**3 + 154*y**2 - 416*y + 314. Let p(m) = -m**3 - 31*m**2 + 83*m - 63. Let f(z) = 3*b(z) + 14*p(z). Solve f(i) = 0.
1, 3, 10
Let d(b) = -2*b**3 - b**2 - 2*b - 9. Let i(w) = -7*w**3 - 3*w**2 - 9*w - 35. Let o(g) = -22*d(g) + 6*i(g). Suppose o(h) = 0. Calculate h.
-3, -1, 2
Let o = 1100 + -618. Let -y**5 - 4*y**5 - o*y**4 + 477*y**4 = 0. Calculate y.
-1, 0
Let x = -263/2 - -137. Let i = 125/22 - x. Find b such that 4/11*b + i*b**2 - 4/11*b**3 + 0 - 2/11*b**4 = 0.
-2, -1, 0, 1
Suppose 0 = -14*k + 3*k - 77. Let w be -2*(k + 25/5). Determine n so that 2/9*n**2 - 2/9*n**3 + 2/9*n**5 - 2/9*n**w + 0 + 0*n = 0.
-1, 0, 1
Let n = 6612 - 46283/7. Factor n*j**2 + 16/7*j + 64/7.
(j + 8)**2/7
Let j(o) = -174*o**2 - 12864*o + 5316. Let a(x) = -11*x**2 - 804*x + 332. Let l(c) = -33*a(c) + 2*j(c). Factor l(r).
3*(r + 54)*(5*r - 2)
Let w(o) be the third derivative of -2/27*o**3 - 1/540*o**6 + 0 + 1/135*o**5 + 13*o**2 + 1/108*o**4 + 0*o. Factor w(h).
-2*(h - 2)*(h - 1)*(h + 1)/9
Suppose -4*b = -1 - 19. Let -4 + 15*c**2 - 6*c**2 + 6*c - b*c**2 - 6*c**2 = 0. What is c?
1, 2
Let t(v) = -v**2 + 2*v + 5. Let j(k) = 2*k**2 - 4*k - 5. Let d(i) = -6*j(i) - 7*t(i). Determine m, given that d(m) = 0.
1
Let k(h) be the first derivative of -8*h**6/15 - 24*h**5/25 - h**4/5 + 2*h**3/5 + h**2/5 - 231. What is d in k(d) = 0?
-1, -1/2, 0, 1/2
Let z(u) be the first derivative of -u**6/18 + 7*u**5/15 - 19*u**4/12 + 25*u**3/9 - 8*u**2/3 + 4*u/3 - 46. Factor z(i).
-(i - 2)**2*(i - 1)**3/3
Let d = 29299/18 - 3255/2. Determine k so that -d*k**2 + 0*k + 8/9 = 0.
-2, 2
Let g be (-39)/25*-5 + -7. Let j(y) be the second derivative of 0 + 0*y**2 + 2/3*y**6 + g*y**5 + 1/3*y**4 + 4/21*y**7 + 0*y**3 + 6*y. Factor j(n).
4*n**2*(n + 1)**2*(2*n + 1)
Factor 11*y**3 + 78*y - 30*y**3 + 14*y**3 - 40 + 3*y**3 - 36*y**2.
-2*(y - 1)**2*(y + 20)
Let q(v) = -19*v**4 + 41*v**3 + 46*v**2 - 20*v. Let w(u) = -u**4 - u**3 - u**2. Let s(f) = q(f) + 6*w(f). Factor s(j).
-5*j*(j - 2)*(j + 1)*(5*j - 2)
Let h(b) = b + 2. Let m be h(0). Factor 0*p**2 + 4*p**m - 8*p**2 - 29 + 24*p - 7.
-4*(p - 3)**2
Let m(s) = -21*s**2 - 6. Let g(w) = 5*w**2 + 1. Let a(y) = -9*g(y) - 2*m(y). Factor a(p).
-3*(p - 1)*(p + 1)
Suppose 4*f = -5*x + 6, 3*x - 11 = -0*x + 5*f. Suppose -d - 1 = 0, -5*d - 2 = -b + 8. Factor -2*s**2 - 12*s**2 + 3*s**2 + x*s + b*s**3.
s*(s - 2)*(5*s - 1)
Let a be 31 - (16 - 2)/2. Let z(u) be the first derivative of 1 + a*u**2 + 4*u**3 + 1/4*u**4 + 64*u. Solve z(s) = 0 for s.
-4
Suppose 3*w = 5*u - 4*u - 190, 0 = 3*w - 4*u + 202. Let a = -123/2 - w. Factor -4 + 10*b + 7/2*b**3 - 9*b**2 - a*b**4.
-(b - 2)**3*(b - 1)/2
Let s(d) = -d**2 - 3*d + d - 2 + 1 + 0. Suppose -5*k + 7 = -8. Let c(n) = 3*n**2 + 6*n + 3. Let q(h) = k*c(h) + 8*s(h). Factor q(i).
(i + 1)**2
Let y(p) be the first derivative of 1/5*p**3 + 0*p + 0*p**2 + 3/20*p**4 - 41. Find g such that y(g) = 0.
-1, 0
Let j(a) = -a**5 + a**4 - a**2. Let s(r) be the first derivative of 0*r**2 - r**3 + 0*r + 0*r**4 + 2 + 1/5*r**5 - r**6. Let d(y) = 4*j(y) - s(y). Factor d(o).
o**2*(o + 1)**2*(2*o - 1)
Factor 1/4*m**2 + 0 - 1/2*m + 1/2*m**3 - 1/4*m**4.
-m*(m - 2)*(m - 1)*(m + 1)/4
Let g = 22 - 18. Suppose -g*s + 3*s + 4 = 0. Factor 2/3*u**3 + 2/3*u**s + 0*u + 0*u**2 + 0.
2*u**3*(u + 1)/3
Let -12*x**4 - 7*x**4 + x**5 + 11*x**3 - 7*x**4 + 14*x**4 = 0. Calculate x.
0, 1, 11
Let n(g) = -g**3 + 24*g**2 + 58*g - 153. Let y be n(26). Let l(b) be the first derivative of 3*b**2 - 3 + 0*b + 2/3*b**y. Factor l(r).
2*r*(r + 3)
Suppose -9*d + 82 = 28. Let k(o) = 6*o**3 + 9*o**2 - 9*o. Let b(n) = 2*n - 1 - n**3 - 2*n**2 + 1. Let p(a) = d*k(a) + 33*b(a). Factor p(v).
3*v*(v - 2)**2
Let n(u) = -12*u**2 - 11*u + 1. Let f(p) = -p + 14. Let g be f(9). Let z(w) = 8*w**2 + 7*w - 1. Let r(x) = g*n(x) + 8*z(x). Factor r(t).
(t + 1)*(4*t - 3)
Let l = -2101 + 2101. Factor 0*g + l + 3/4*g**2.
3*g**2/4
Suppose 2*g + 72 = 8*g. Let t be 6/(-4)*(-7)/(441/g). Factor -2/7*m**2 + 2/7*m**3 + t*m**4 - 2/7*m + 0.
2*m*(m - 1)*(m + 1)**2/7
Suppose -11*t = 15*t - 7*t. Let f(a) be the first derivative of 2/7*a**2 - 4 + t*a**3 + 2/7*a - 1/7*a**4 - 2/35*a**5. Factor f(k).
-2*(k - 1)*(k + 1)**3/7
Let s(l) be the second derivative of l**6/40 + 21*l**5/80 - l**4/2 + 68*l. Let s(o) = 0. What is o?
-8, 0, 1
Let w(p) be the first derivative of 8 + 1/540*p**6 - 1/3*p**3 - 1/36*p**4 + 0*p**2 + 0*p + 0*p**5. Let o(g) be the third derivative of w(g). Solve o(a) = 0.
-1, 1
Let t(y) be the third derivative of -y**5/240 - 7*y**4/24 + 237*y**2 + 2*y. Let t(w) = 0. What is w?
-28, 0
Let m = 101202/11 - 9200. Suppose 4*q - 3*q = 0. Solve -2/11*u + q + m*u**5 + 4/11*u**4 + 0*u**3 - 4/11*u**2 = 0 for u.
-1, 0, 1
Let n be (-280)/(-525) - 2/10. Determine w, given that -1/3*w**2 + 1/3*w + 1/3 - n*w**3 = 0.
-1, 1
Let s be 0 + 316/168 + 1 - 2. Let v = s + -3/14. Determine y so that -2/3*y**3 - v*y**4 + 0 + 2/3*y**2 + 2/3*y = 0.
-1, 0, 1
Let l(x) = -26*x**3 + 168*x**2 - 94*x - 3916. Let b(f) = -9*f**3 + 56*f**2 - 31*f - 1306. Let n(r) = -14*b(r) + 5*l(r). Factor n(p).
-4*(p - 9)**2*(p + 4)
Let s(n) be the first derivative of n**5/10 + n**4/3 + n**3/3 - 4*n + 7. Let q(l) be the first derivative of s(l). Let q(x) = 0. What is x?
-1, 0
Determine h so that 88/7*h**4 + 648/7 + 1476/7*h - 349/7*h**3 - 514/7*h**2 - 5/7*h**5 = 0.
-2, -2/5, 2, 9
Factor -1/3*o**2 + 0 - 16/3*o.
-o*(o + 16)/3
Let r(z) be the first derivative of -16/3*z**5 + 80/9*z**3 - 35/18*z**6 + 5/4*z**4 + 14 + 10/3*z**2 + 0*z. Suppose r(s) = 0. What is s?
-2, -1, -2/7, 0, 1
Let x = 2129/2 - 1064. Factor 1/2 + 3/2*g**3 + x*g - 5/2*g**2.
(g - 1)**2*(3*g + 1)/2
Let d = -3860 + 3863. Determine u, given that -8/17*u**4 - 6/17*u**d - 2/17*u**5 + 8/17*u**2 + 0 + 8/17*u = 0.
-2, -1, 0, 1
Suppose -125*o - 32 = -127*o. Let s be (o/55)/((-8)/(-20)). Find k, given that 2/11*k**5 - 4/11 + 8/11*k**3 + s*k**4 - 10/11*k - 4/11*k**2 = 0.
-2, -1, 1
Suppose -2*h + 20 = 4*l, 3*l - 2 - 4 = 3*h. Let u = l - 1. Solve -6*z**u - 4*z**4 + 6*z**2 + 6*z + z**4 - 3*z**2 = 0 for z.
-2, -1, 0, 1
Suppose 6*d - 3*r - 18 = 3*d, -d + 3*r + 12 = 0. Factor 10/3*a**d + 8/15*a + 8/3*a**2 + 0.
2*a*(5*a + 2)**2/15
Factor -98/15*r**3 + 32/5*r - 24/5 + 14/3*r**2.
-2*(r + 1)*(7*r - 6)**2/15
Let g(i) be the third derivative of -4*i**2 - 1/840*i**8 + 16/15*i**3 + 3/175*i**7 + 28/75*i**5 + 9*i - 4/5*i**4 - 8/75*i**6 + 0. Solve g(x) = 0.
1, 2
Factor -o - 5 - 718*o**2 + 3 + 719*o**2 + 2.
o*(o - 1)
Let f = -36 + 104. Let w = 100 - f. Factor -q**4 + 2*q**2 - w*q + 32*q - 1.
-(q - 1)**2*(q + 1)**2
Let g(h) be the first derivative of 0*h**4 + 1/5*h**5 + h - 3 + 0*h**2 - 2/3*h**3. Factor g(i).
(i - 1)**2*(i + 1)**2
Let c(a) be the third derivative of 5*a**5/6 + 377*a**4/60 + 2*a**3/5 + 3*a**2 - 108. Factor c(f).
2*(f + 3)*(125*f + 2)/5
Let n = -12 - -10. Let i(y) = y**2 + 2*y + 3. Let k be i(n). Determine u so that -25*u**5 - 8*u - 12*u**2 - u**4 + 28*u**k + 5*u**5 + 13*u**4 = 0.
-1, -2/5, 0, 1
Let d(q) be the first derivative of 2*q**6/3 + 12*q**5 + 27*q**4 - 324*q**3 - 7. Factor d(z).
4*z**2*(z - 3)*(z + 9)**2
Let p(g) = g. Let m = 1 - -1. Let u(r) = 2*r**2 + 2*r + 2. Let o(d) = m*u(d) + 4*p(d). Factor o(x).
4*(x + 1)**2
Suppose 509*h + 6 = -5*r + 511*h, 0 = 3*r + 3*h - 30. Let 1/7*o**r + 2/7*o + 0 = 0. Calculate o.
-2, 0
Factor 122 - 30*g + 2*g**4 - 69*g - 10 - 59*g + 342*g**2 - 180*g - 118*g**3.
2*(g - 56)*(g - 1)**3
Let r(l) = -7*l**2 + 4. Let k be r(-2). Let y be (-19 - k)*6/40. Factor 3/2*q + 3/4 + y*q**2.
3*(q + 1)**2/4
Let w(m) be the first derivative of m**6/48 - m**5/40 - 3*m**4/32 + m**3/24 + m**2/8 - 50. Factor w(k).
k*(k - 2)*(k - 1)*(k + 1)**2/8
Let k(r) = 4 + 2 - 7. Let s(z) = z**2 - z - 1. Suppose -n + 1 = -2*g, g + n = -3*n - 5. Let a(v) = g*k(v) + s(v). Let a(h) = 0. Calculate h.
0, 1
Let s(g) be the third derivative of g**6/150 + 3*g**5/25 + 2*g**4/3 + 8*g**3/5 - 587*g**2. Factor s(f).
4*(f + 1)*(f + 2)*(f + 6)/5
Suppose 0 = 3*f + 5 - 2. Let p = f + 3. Factor -b**2 + 0*b - 3*b**3 + 3*b + p*b + 2 - 2*b - b**4.
-(b - 1)*(b + 1)**2*(b + 2)
Let g = 6141 - 6138. Factor 4/3*n**g - 8/9*n**2 + 2/9*n + 0 + 2/9*n**5 - 8/9*n**4.
2*n*(n - 1)**4/9
Let k be (520/(-1092))/((-10)/28)