8. Let i = n - -7. Factor -8/3*r**3 + 4/3*r**2 - 5/3*r**4 + 0*r + i.
-r**2*(r + 2)*(5*r - 2)/3
Let i(x) be the third derivative of 0*x - 1/12*x**3 - 1/672*x**8 + 1/60*x**5 + 0 + 16*x**2 + 1/120*x**6 - 1/48*x**4 - 1/420*x**7. Factor i(z).
-(z - 1)**2*(z + 1)**3/2
Let t(y) be the third derivative of -y**8/288 - 4*y**7/315 + y**6/9 + 5*y**5/12 - 17*y**4/16 - 3*y**3/2 + 56*y**2 - 3*y. Let t(a) = 0. Calculate a.
-3, -2/7, 1, 3
Let p(s) = s**2 + 3*s. Let y(u) = 4*u**2 + 46*u + 11. Let l(m) = m**2 + 9*m + 2. Let x(j) = 11*l(j) - 2*y(j). Let f(i) = -5*p(i) + 2*x(i). Factor f(a).
a*(a - 1)
Suppose 5*z + 0*z + 4*r = 60, 0 = 4*z + 5*r - 57. Let k be 4/z + (-15)/(-6). Factor 40/11*l**2 + 14/11*l**4 - 16/11*l + 0 - 2/11*l**5 - 36/11*l**k.
-2*l*(l - 2)**3*(l - 1)/11
Suppose 446*g + 12 = i + 448*g, -4*i + 4*g = 24. Suppose 1/3*p**2 + i - 8/3*p = 0. What is p?
0, 8
Let v(r) be the first derivative of -r**3/3 + 5*r**2 - 19*r + 11. Let y be v(3). Solve 2/9*w**2 - 4/3*w + y = 0.
3
Let i(g) be the second derivative of 0*g**3 + 5/42*g**7 - g**5 + 0*g**2 + 7*g - 1/6*g**6 + 5/3*g**4 + 0. Factor i(t).
5*t**2*(t - 2)*(t - 1)*(t + 2)
Let a(z) = z**3 - 4*z**2 - 11*z - 4. Let g be a(6). Factor -m**2 + 3*m**g + 98*m**3 - 92*m**3 - 6*m - 2.
2*(m - 1)*(m + 1)*(3*m + 1)
Let l(z) = 5*z**3 + 31*z**2 + 70*z + 53. Let c(t) = t**3 + 3*t**2 + 1. Let p(w) = 6*c(w) - 2*l(w). Determine a, given that p(a) = 0.
-5, -1
Find t such that 24/13*t**2 + 18/13*t**3 + 8/13*t + 0 = 0.
-2/3, 0
Factor 16 + 1/2*c**4 + 4*c - 7*c**3 - 14*c**2 + 1/2*c**5.
(c - 4)*(c - 1)*(c + 2)**3/2
Let u(q) be the second derivative of q**6/40 - 3*q**5/80 - 5*q**4/16 - 3*q**3/8 + 13*q + 3. Determine d, given that u(d) = 0.
-1, 0, 3
Let t(r) be the second derivative of -r**6/1080 - r**5/360 - 5*r**3/6 - 11*r. Let w(y) be the second derivative of t(y). Suppose w(a) = 0. Calculate a.
-1, 0
Suppose 4 = 3*k - 5*d + 9, -40 = -4*k - 5*d. Let t(x) be the third derivative of 1/30*x**k - 2*x**2 + 0*x + 1/300*x**6 + 4/15*x**3 + 0 + 2/15*x**4. Factor t(s).
2*(s + 1)*(s + 2)**2/5
Let b be 3 - -1 - (-16 - (-649)/33). Determine u, given that -1/6*u - 1/3*u**2 + 1/6*u**5 + b*u**4 + 0*u**3 + 0 = 0.
-1, 0, 1
Let t(v) be the first derivative of -v**5/5 - v**4 + 2*v**3/3 + 6*v**2 - 9*v + 109. What is h in t(h) = 0?
-3, 1
Let d(o) be the second derivative of -o**6/200 + o**5/50 + o**4/40 - o**3/5 + o**2 - 10*o. Let z(q) be the first derivative of d(q). Solve z(a) = 0 for a.
-1, 1, 2
Factor 1/5*r**2 + 4/5 + 4/5*r.
(r + 2)**2/5
Let w(t) = t**2 - 38*t - 477. Let f be w(48). Factor -a**2 + 1/3*a**4 + 1/3*a**f - 1/3*a + 2/3.
(a - 1)**2*(a + 1)*(a + 2)/3
Let 2*n**3 + 38*n**2 - 14*n + 0*n - 12 - 38*n**2 = 0. Calculate n.
-2, -1, 3
Let q(d) = d**2 - 21*d + 110. Let k be q(10). Solve -6/7*c**3 + k*c + 4/7*c**2 + 2/7*c**5 + 0 + 0*c**4 = 0 for c.
-2, 0, 1
Suppose -16 = 3*h - 7*h - 2*y, 0 = -h + 3*y - 10. Let j(o) be the first derivative of -8 + 0*o + 2/45*o**3 - 2/15*o**h. Factor j(n).
2*n*(n - 2)/15
Let n(l) = l**2 + 127*l + 58. Let h(k) = -k**2 - 2*k + 1. Let c(x) = 6*h(x) + 2*n(x). Determine g so that c(g) = 0.
-1/2, 61
Suppose f**4 - 15*f**3 - 325 + 654 - 16*f**2 - 329 = 0. Calculate f.
-1, 0, 16
Let w(s) be the second derivative of 5/18*s**4 + 0*s**6 + 0*s**2 - 5/126*s**7 + 1/4*s**5 + 24*s + 0*s**3 + 0. Let w(g) = 0. Calculate g.
-1, 0, 2
Factor 80/3 - 2/3*q**2 + 26*q.
-2*(q - 40)*(q + 1)/3
Let k(j) be the first derivative of -2 + 3/5*j + 3/5*j**4 + 6/5*j**2 + 6/5*j**3 + 3/25*j**5. What is g in k(g) = 0?
-1
Let d(u) be the first derivative of -26 + 8*u + 7/4*u**4 - 2/3*u**3 - 14*u**2. Suppose d(i) = 0. Calculate i.
-2, 2/7, 2
Let o be 7/(-1) + (-9)/(-3) - -244. Find s, given that 240 + 3*s**2 - o + 10*s - s = 0.
-3, 0
Factor 5300*o + 4602*o**3 + 9248 - 132*o - 4598*o**3 + 280*o**2.
4*(o + 2)*(o + 34)**2
Let s(z) = 13*z**3 - 79*z**2 + 194*z - 288. Let x(l) = -9*l**3 + 53*l**2 - 126*l + 192. Let k(o) = 5*s(o) + 7*x(o). Factor k(i).
2*(i - 6)*(i - 4)*(i - 2)
Let q(g) be the second derivative of g**6/70 - 3*g**5/28 - 13*g**4/28 - g**3/2 + 69*g. Solve q(n) = 0 for n.
-1, 0, 7
Let b(r) be the second derivative of r**4/6 - 4*r**3/3 - 5*r**2 - 4*r - 37. Factor b(q).
2*(q - 5)*(q + 1)
Let u(c) be the third derivative of -c**5/30 + c**4/2 - 3*c**3 + 2*c**2 + 65*c. Factor u(i).
-2*(i - 3)**2
Let t = 10 - 7. Let l(o) = -12*o**2 + 6*o. Let x(m) = -m**2 - m. Suppose 11*s - 13*s + 2 = 0. Let j(p) = s*l(p) + t*x(p). Factor j(v).
-3*v*(5*v - 1)
Suppose -105 + 210 - 675*z - 12*z**5 + 27*z**5 + 165 + 100*z**3 + 73*z**4 - 450*z**2 + 27*z**4 = 0. Calculate z.
-3, 1/3, 2
Suppose 2*f + 9*r = 11*r + 12, 7*r + 42 = -5*f. Determine h so that 0*h**4 + 1/6*h**5 - 1/2*h + 4/3*h**2 + f - h**3 = 0.
-3, 0, 1
Let y(o) be the third derivative of o**5/12 - 40*o**4 + 7680*o**3 - 90*o**2 - 2. Factor y(b).
5*(b - 96)**2
Let l(a) be the first derivative of -2*a**3/21 + 18*a/7 - 59. What is b in l(b) = 0?
-3, 3
Determine n so that 0 - 4/3*n - 19*n**4 + 89/3*n**3 - 28/3*n**2 = 0.
-2/19, 0, 2/3, 1
Let n = -18 - -27. Find z, given that -6*z**2 + 6*z**3 + z + n*z**2 - 6*z**2 - 4*z = 0.
-1/2, 0, 1
Let y(b) be the third derivative of b**5/90 - b**4/4 - b**2 + 59. Factor y(t).
2*t*(t - 9)/3
Let t(a) = -a**3 - 3*a**2 - 3*a - 2. Let l be t(-2). Suppose l = -0*i - 17*i + 85. Factor 2*n**4 + 0 + 16/7*n + 2/7*n**i + 36/7*n**3 + 40/7*n**2.
2*n*(n + 1)*(n + 2)**3/7
Let p(z) be the first derivative of -z**5/5 - z**4 - 2*z**3 - 2*z**2 - 4*z - 1. Let f(x) be the first derivative of p(x). Find k such that f(k) = 0.
-1
Let h(z) be the third derivative of 1/56*z**4 + 0*z**3 + 0 + 1/1470*z**7 + 0*z + 15*z**2 - 1/280*z**6 - 1/420*z**5. Factor h(u).
u*(u - 3)*(u - 1)*(u + 1)/7
Let c(d) = 7*d**4 - 16*d**3 - 4*d**2 + 4*d - 8. Let s(y) = -8*y**4 + 17*y**3 + 5*y**2 - 5*y + 10. Let j(r) = 5*c(r) + 4*s(r). Factor j(z).
3*z**3*(z - 4)
Let y = 1718 - 1715. Find f such that 0*f**2 - 1/3*f**4 + 0 + 0*f + 0*f**y = 0.
0
Factor -12/19*i**3 + 2/19*i**4 - 50/19*i**2 + 0 - 36/19*i.
2*i*(i - 9)*(i + 1)*(i + 2)/19
Let w(y) be the third derivative of -y**5/60 + y**4/3 + 3*y**3/2 + 85*y**2. Factor w(t).
-(t - 9)*(t + 1)
Let v be 3/((-9)/(-24)) - 4. Let f(a) be the third derivative of -1/660*a**6 + 0*a**3 + 0 + 0*a - 1/33*a**v + 10*a**2 - 2/165*a**5. Factor f(b).
-2*b*(b + 2)**2/11
Suppose 5*l**2 - 3*l**2 + 91*l - 103*l - 6*l**2 = 0. What is l?
-3, 0
Factor -4/7*d**4 + 0 + 0*d - 144/7*d**2 + 48/7*d**3.
-4*d**2*(d - 6)**2/7
Let h(f) = f**3 - 22*f**2 + 18*f + 65. Let p be h(21). Factor -3/5*k + 0 + 3/5*k**p.
3*k*(k - 1)/5
Let o be (-174)/(-588)*7 - 10/(-4). Factor -16/7*z - o - 2/7*z**2.
-2*(z + 4)**2/7
Suppose -6 = -5*n + 2*a, -3*a + 0 + 12 = 3*n. Find g such that 142 - 107 - 40*g - g**2 + 6*g**n = 0.
1, 7
Let x(r) be the first derivative of -8*r**5/15 + 49*r**4/3 - 416*r**3/3 + 96*r**2 - 116. Factor x(g).
-4*g*(g - 12)**2*(2*g - 1)/3
Let s = -127 - -127. Let t(l) be the third derivative of -1/90*l**5 + s + 0*l - 1/18*l**4 + 0*l**3 + 3*l**2. Find f such that t(f) = 0.
-2, 0
Let q(y) be the first derivative of -2/35*y**5 + 16/7*y**3 - 25 + 18/7*y - 3/7*y**4 - 26/7*y**2. Factor q(g).
-2*(g - 1)**3*(g + 9)/7
Let z(l) be the first derivative of l**5/20 - 3*l**4/16 + l**2/2 + 763. Determine c so that z(c) = 0.
-1, 0, 2
Let w = -30 - -41. Find t, given that w + 17*t - 4 + 5*t**2 + 3 - 32*t = 0.
1, 2
Let z(v) be the second derivative of -2*v**6/15 + v**5/20 + 143*v. Factor z(y).
-y**3*(4*y - 1)
Let l(u) be the third derivative of 0*u**4 + 0*u**3 + 0*u + 0*u**5 - 1/150*u**6 - 17*u**2 + 2/105*u**7 + 1/70*u**8 + 0. Factor l(p).
4*p**3*(p + 1)*(6*p - 1)/5
Let s(f) = f**2 + 1. Let k(g) be the third derivative of -g**2 + 0 - 1/120*g**6 + 0*g - 2/15*g**5 - 7/6*g**3 + 0*g**4. Let c(q) = 4*k(q) + 28*s(q). Factor c(a).
-4*a**2*(a + 1)
Find p such that -15488/3 + 352/3*p - 2/3*p**2 = 0.
88
Let p(n) = n**2 + 13*n + 14. Let a be p(-12). Factor -30*i**3 - 2*i**5 - 2917*i + 18*i**a + 2917*i + 14*i**4.
-2*i**2*(i - 3)**2*(i - 1)
Let z = -1316/5 + 264. Suppose 5*k + 10 = 4*n, -14 = -2*k + 5*k - 4*n. Factor -2/5*h + 4/5*h**k - z + 2/5*h**3.
2*(h - 1)*(h + 1)*(h + 2)/5
Let k be (-18)/(-8) + (8/(-4))/8. Suppose -3*b + 9 = k*g, 2*g = 4*g. Find y such that -9*y**2 - 1/3 + b*y + 9*y**3 = 0.
1/3
Let r(t) be the third derivative of t**6/120 - 13*t**4/2