470. Factor 0 + d*u + 2/3*u**2.
2*u**2/3
Factor -8/9*p + 16/3 + 2/9*p**4 - 20/9*p**2 + 2/9*p**3.
2*(p - 2)**2*(p + 2)*(p + 3)/9
Let z(j) = -4*j**3 - 7*j**2 + 5*j + 11. Let r be z(-4). Factor -s**3 - 4048*s - s**3 + r*s**2 - 91*s**2 + 134*s**2 + 3872.
-2*(s - 44)**2*(s - 1)
Suppose 116*n + 10 = 242. Let o(q) be the second derivative of 5/4*q**4 - 5/4*q**5 + 5/3*q**3 + 0 - 13*q + 0*q**n. Determine l, given that o(l) = 0.
-2/5, 0, 1
Let n(k) = -k**4 - k**3 + k**2 + 1. Let i(w) = -5*w**5 - 26*w**4 - 26*w**3 + 16*w**2 + 25*w + 16. Let j = -62 + 68. Let o(h) = j*n(h) - i(h). Factor o(x).
5*(x - 1)*(x + 1)**3*(x + 2)
Let x(t) be the third derivative of -t**6/60 + 2063*t**5/10 - 4255969*t**4/4 + 8780064047*t**3/3 + 2*t**2 + 2134*t. Solve x(f) = 0 for f.
2063
Suppose -3946250*d**2 + 165*d + 8*d**3 + 180 - 3*d**3 + 3946300*d**2 = 0. Calculate d.
-4, -3
Let f(l) be the second derivative of l**5/130 - 2*l**4/3 + 52*l**3/3 + 1492*l. Factor f(t).
2*t*(t - 26)**2/13
Suppose -6*m + 5*f + 177 = -5*m, -5*m + 4*f + 780 = 0. Let p = -152 + m. Let 2/5*h**2 + 4/5*h + p = 0. What is h?
-2, 0
Let i(h) be the first derivative of -6 - 2*h**2 - 2/27*h**3 - 18*h. Factor i(m).
-2*(m + 9)**2/9
Let y(f) = f**3 - 64*f**2 + 631*f - 908. Let i be y(10). What is k in 0 - 1369/6*k**i - 37/3*k**3 + 0*k - 1/6*k**4 = 0?
-37, 0
Suppose 3*p - 6*l - 944 = -7*l, -p + 5*l = -288. Let s = p - 310. Suppose 0*u**2 + 2/3*u**5 + 0 + 0*u + 2/3*u**4 + 0*u**s = 0. What is u?
-1, 0
Let q = -31 - -36. Factor -432*y + 7 + 437*y + 23 - q*y**2.
-5*(y - 3)*(y + 2)
Let y(k) be the third derivative of -k**8/280 + 12*k**7/175 - 8*k**6/25 - 7*k**5/5 + 45*k**4/4 + 50*k**3 - 189*k**2 - 7*k. Find q such that y(q) = 0.
-2, -1, 5
Let s(q) = q**4 + 195*q**3 - 2831*q**2 + 3965*q + 166706. Let m(l) = -2*l**4 - 201*l**3 + 2830*l**2 - 3964*l - 166708. Let b(j) = 4*m(j) + 5*s(j). Factor b(x).
-3*(x - 21)**3*(x + 6)
Let n = -23 - -27. Suppose -n*f - 11 = -35. Let o(z) = 9*z**2 + z - 6. Let k(i) = -8*i**2 - 2*i + 7. Let u(v) = f*k(v) + 7*o(v). Factor u(a).
5*a*(3*a - 1)
Let s(q) be the second derivative of -1/120*q**6 + 0 - 5/16*q**4 + 175/24*q**3 - 11/80*q**5 + 173*q + 125/2*q**2. Factor s(u).
-(u - 4)*(u + 5)**3/4
Let f(s) = 20*s**2 + 1680*s + 117614. Let j(h) = 7*h**2 + 560*h + 39205. Let q(c) = 5*f(c) - 14*j(c). Factor q(t).
2*(t + 140)**2
Factor 93/7*x**3 + 0 + 3/7*x**4 - 222/7*x**2 - 792/7*x.
3*x*(x - 4)*(x + 2)*(x + 33)/7
Determine p, given that 86*p - 2969 + 881 + 3*p**2 - 59*p - 12*p = 0.
-29, 24
Determine k, given that 812/3*k**4 - 2108/3*k**2 + 432 - 92/3*k**3 + 96*k - 196/3*k**5 = 0.
-1, 1, 18/7
Let a(o) be the first derivative of -101 + 0*o - 1/3*o**3 - 2*o**2. Find v such that a(v) = 0.
-4, 0
Suppose -3*r = -4*l + 60, 4*l = 5*r - 3711 + 3803. Factor 2/11*g**l - 8/11*g**2 + 8/11 - 2/11*g.
2*(g - 4)*(g - 1)*(g + 1)/11
Let k(m) be the second derivative of m**9/10584 + m**8/588 + m**7/105 + 2*m**6/105 - m**3/6 + 59*m. Let y(x) be the second derivative of k(x). Factor y(v).
2*v**2*(v + 2)**2*(v + 6)/7
Let v(n) be the first derivative of n**5 + 5*n**4/4 - 95*n**3/3 + 55*n**2/2 + 150*n + 8204. Determine h so that v(h) = 0.
-5, -1, 2, 3
Let y(o) = 15*o**3 + 60*o**2 + 11*o. Suppose 3*p + 44 = -p. Let n(b) = 19*b**2 - 57*b + 5*b**3 - b**2 + 61*b + 2*b**2. Let m(r) = p*n(r) + 4*y(r). Factor m(l).
5*l**2*(l + 4)
Let a(h) be the first derivative of -h**6/60 + 17*h**5/90 + 2*h**4/9 + 20*h**3/3 + 3*h - 214. Let n(f) be the third derivative of a(f). Factor n(q).
-2*(q - 4)*(9*q + 2)/3
Suppose -24 = 78*a - 80*a. Suppose 4*d = a + 36. Factor -d*s + 2/3*s**2 + 54.
2*(s - 9)**2/3
Let t(o) be the first derivative of -1/2*o**2 + 0*o + 1/9*o**3 - 2. Determine c, given that t(c) = 0.
0, 3
Let m(o) = -5*o**2 + 421*o + 11233. Let z(b) = -8*b**2 + 420*b + 11232. Suppose 5*u = 11*v - 9*v - 26, 3*u + 9 = -v. Let d(a) = u*m(a) + 3*z(a). Factor d(t).
-4*(t + 53)**2
Let z(m) = -2*m**4 - 4*m**3 - m**2 - m - 1. Let h(t) = 23*t**4 + 412*t**3 + 14212*t**2 + 157102*t + 143269. Let g(s) = -h(s) - 10*z(s). What is f in g(f) = 0?
-53, -17, -1
Suppose 103*y**2 - 48*y**2 + 1849 - 51*y**2 + 1387 + 2020*y - 1220 = 0. What is y?
-504, -1
Let f(s) be the first derivative of 1/14*s**4 - 11 - 4*s**3 + 84*s**2 - 784*s. Factor f(m).
2*(m - 14)**3/7
Let v(h) = h**2 - 1. Suppose 8 = 2*m - 6*m + 4*z, 0 = -m - z - 2. Let j(g) = 4*g**3 + 78*g**2 + 2. Let l(s) = m*v(s) - j(s). Find y, given that l(y) = 0.
-20, 0
Let t(j) be the third derivative of -j**9/432 + j**8/672 + j**7/18 - j**6/18 + j**4/2 - 2*j**2 - 16*j. Let d(n) be the second derivative of t(n). Factor d(u).
-5*u*(u - 2)*(u + 2)*(7*u - 2)
Suppose 44*m = 8122 - 1522. Let r be (-15)/m*(0 + -3 + 1). Suppose -4/5 - r*b**2 - b = 0. Calculate b.
-4, -1
Let b(i) be the second derivative of i**6/10 + 39*i**5/80 + 15*i**4/16 + 7*i**3/8 + 3*i**2/8 + 29*i + 6. Factor b(h).
3*(h + 1)**3*(4*h + 1)/4
Suppose 4*b - 133 - 7 = 2*s, 3*b = 3*s + 108. Let j(i) = -20*i + 48 - 60 + b + 5*i**2. Let g(a) = 2*a**2 - 7*a + 7. Let r(t) = -7*g(t) + 2*j(t). Factor r(h).
-(h - 1)*(4*h - 5)
Let g(d) = -4*d**2 - 80*d + 2. Let b be g(0). Factor 0*r - 4/3 + 4/3*r**b.
4*(r - 1)*(r + 1)/3
Let f(h) = h**2 + 8*h + 2. Let t be f(-8). Suppose -5*p + t*x = -22, -15*p = -18*p - 4*x + 8. Factor -3/5*n**p - 9/5*n**3 + 0*n + 0*n**2 + 0.
-3*n**3*(n + 3)/5
Let m(u) be the second derivative of 17*u**4/24 + 19*u**3/6 + 2*u**2 + 11*u + 22. Determine q so that m(q) = 0.
-2, -4/17
Let h(m) be the second derivative of 0 + 3/70*m**5 - 156/7*m**2 + 139*m - 9/14*m**4 - 48/7*m**3. Suppose h(a) = 0. Calculate a.
-2, 13
Factor -1/2*z**2 - 315/2*z + 0.
-z*(z + 315)/2
Suppose -10*n = 29*n - 117. Suppose 229*w - 3*z = 230*w + n, -3*z = -w + 3. Factor w*r**2 + 0*r + 0 - 1/2*r**5 - 2*r**3 - 2*r**4.
-r**3*(r + 2)**2/2
Factor 31*q**2 + 15*q**2 + 340*q + 28*q**2 - 3*q**3 + 22*q**2 - 432 - q**3.
-4*(q - 27)*(q - 1)*(q + 4)
Let g(b) be the first derivative of b**6/90 + b**5/15 - 35*b**4/6 + 2*b**3/3 - 195. Let k(q) be the third derivative of g(q). Factor k(l).
4*(l - 5)*(l + 7)
Let y = -911 - -915. Factor 47*d - 79*d - 66*d**3 + 13*d**4 + 127*d**2 + 27 - 9*d**2 - 61*d - d**5 + 2*d**y.
-(d - 9)*(d - 3)*(d - 1)**3
Let i be ((-1)/1 + 2)*14. Let w be 14/i + (1 - -1). Factor -25*a - 5*a**w + 0*a**3 + 10 - 15*a**2 + 35*a**2.
-5*(a - 2)*(a - 1)**2
Let i be (((-12)/9)/(10/(-15)))/((-81)/(5589/(-46))). Factor -2/5*g**5 + 4/5*g**4 + 0 + 6/5*g**i - 8/5*g**2 - 8/5*g.
-2*g*(g - 2)**2*(g + 1)**2/5
Find q such that -8*q**4 + 0 - 1113/2*q**2 + 139/2*q + 1116*q**3 = 0.
0, 1/4, 139
Let k(w) = w**3 - 2*w**2 - 7*w + 1. Let d be k(4). Suppose d*v + 61 = 4*p, -4*v = -0 + 4. Factor p*f + 14*f**2 - 15*f - 5*f**2 - 8*f**3.
-f*(f - 1)*(8*f - 1)
Let u(k) be the second derivative of k**5/5 + 46*k**4/3 - 290*k**3/3 + 196*k**2 + 16*k - 16. Find r such that u(r) = 0.
-49, 1, 2
Let j(w) be the second derivative of -w**5/20 + 77*w**4/12 - 146*w**3/3 - 2649*w. Suppose j(d) = 0. What is d?
0, 4, 73
Let i = -203680 + 203683. Determine f, given that 103/3*f - 1/3*f**4 + 79/3*f**2 + 14 + 17/3*f**i = 0.
-2, -1, 21
Let r(s) = -5*s - 12. Let k be r(-6). Let h be 12/(-54) - (-40)/k. Factor h*v + 22*v**2 + 9*v**2 + 78*v + 20 + 4*v**2.
5*(v + 2)*(7*v + 2)
Let g(i) be the first derivative of 43 - 4/3*i**3 - 10*i**2 + 24*i. Let g(u) = 0. What is u?
-6, 1
Suppose -1001*k + 996*k = -10. Factor 5/3 + 5/6*p**k + 5/2*p.
5*(p + 1)*(p + 2)/6
Let w be 243/135 + 187/385. Determine l so that -l**2 + w + 1/7*l**3 + 8/7*l = 0.
-1, 4
Let j(x) be the third derivative of -15*x**8/112 - 4*x**7/7 + 61*x**6/12 + 22*x**5/3 + 25*x**4/8 + 817*x**2 - 1. Suppose j(d) = 0. What is d?
-5, -1/3, 0, 3
Let g = -16817 + 16821. Let x(h) be the third derivative of -25*h**2 + 0*h**3 - 7/24*h**6 + 5/42*h**7 + 1/4*h**5 + 0*h**g + 0*h - 5/336*h**8 + 0. Factor x(i).
-5*i**2*(i - 3)*(i - 1)**2
Let l(b) be the first derivative of b**4/4 + 158*b**3 + 945*b**2/2 + 472*b + 1843. What is v in l(v) = 0?
-472, -1
Let q(a) be the first derivative of -54*a**2 - 66*a**3 - 18/5*a**5 + 1/6*a**6 + 107/4*a**4 + 216*a + 141. Solve q(s) = 0 for s.
-1, 1, 6
Let 4360*u**2 + 5*u**5 - 1545*u**3 - 83*u**4 - 508665*u + 223*u**4 + 505705*u = 0. What is u?
-37, 0, 1, 4
Let a(b) be the second derivative of -b**5/70 - 25*b**4/14 - 86*b**3/3 - 528*b**2/7 + 9686*b. Fact