8. Suppose 100/3*a**4 + 10/3 - q*a**5 + 20/3*a**3 - 110/3*a**2 + 35/3*a = 0. Calculate a.
-1, -2/11, 1
What is d in -51*d**3 - 773/5*d - 771/5*d**2 + 1/5*d**4 - 258/5 = 0?
-1, 258
Determine y so that 1510*y**2 - 14*y - 44*y - 56*y + 21*y**3 - 1117*y**2 = 0.
-19, 0, 2/7
Let x(g) = 7*g**3 + 390*g**2 + 9627*g + 61254. Let t(p) = -50*p**3 - 2725*p**2 - 67390*p - 428780. Let a(j) = -2*t(j) - 15*x(j). Factor a(m).
-5*(m + 10)*(m + 35)**2
Let k be ((-4)/(-181 - -1))/(72/15). Let w(y) be the third derivative of 0*y + 0 - 1/1080*y**6 - 16*y**2 + k*y**4 + 0*y**5 + 0*y**3. Let w(g) = 0. What is g?
-1, 0, 1
Let q(t) be the second derivative of -t**6/105 - 127*t**5/70 - 1984*t**4/21 + 4096*t**3/21 - 42*t - 3. Suppose q(u) = 0. Calculate u.
-64, 0, 1
Let k(n) be the third derivative of -n**8/5040 + 3*n**7/70 - 81*n**6/20 + 19*n**5/10 - 67*n**2. Let q(c) be the third derivative of k(c). Factor q(z).
-4*(z - 27)**2
Let b(s) = s**3 - 7*s**2 + 7*s - 4. Let m be b(6). Let o = 5992006/3495345 - -2/499335. Factor -o*r**m - 4/7*r**3 - 8/7*r + 0.
-4*r*(r + 1)*(r + 2)/7
Factor -2*r**5 - 33627*r**3 + 25*r**4 + 40*r + 33597*r**3 - 20*r**2 - 3*r**5.
-5*r*(r - 2)**3*(r + 1)
Factor -13*j**2 + j**2 - j**4 - 103*j**3 + 18 + 96*j**3 - j**2 + 3*j.
-(j - 1)*(j + 2)*(j + 3)**2
Let s(w) be the second derivative of -w**6/150 + 3*w**5/100 + 3*w**4/4 + 77*w**3/30 + 18*w**2/5 - 5*w - 16. Factor s(q).
-(q - 9)*(q + 1)**2*(q + 4)/5
Factor -733*c + 0 + 731/2*c**2 + 1/2*c**3.
c*(c - 2)*(c + 733)/2
Suppose 0 = -3*z + 18*q - 16*q + 20, q - 36 = -10*z. Let t(u) be the second derivative of -8/39*u**3 - 7/13*u**2 + 0 - 1/78*u**z - 6*u. Factor t(k).
-2*(k + 1)*(k + 7)/13
Let h(j) be the first derivative of 3*j**5/35 - j**4/2 - 5*j**3/21 - 1365. Solve h(f) = 0 for f.
-1/3, 0, 5
Suppose 3 + 7 = 5*w. Let m be (8/14)/((-8)/(-28)). Let -8 - 119*y**4 - 100*y - 108*y**w - 324*y**m - 87*y**4 - 50*y**4 - 704*y**3 = 0. What is y?
-2, -1/4
Suppose -80 = -4*y + 4*z, 7*z + 35 = y + 3*z. Let t(b) = -b + 1. Let q(m) = 12*m**3 - 9*m**2 - 60*m - 33. Let j(r) = y*t(r) + q(r). Factor j(v).
3*(v - 3)*(v + 2)*(4*v + 1)
Let y be ((-1)/((-3)/(-17)) + 9)*(-126)/(-70). Factor -14*u + y*u**2 + 22/3 + 2/3*u**3.
2*(u - 1)**2*(u + 11)/3
Let r(l) be the second derivative of -l**4/3 + 62*l**3/3 + 5*l + 696. Determine p, given that r(p) = 0.
0, 31
Let q(j) be the third derivative of 4*j**2 + 0*j + 1 + 49/60*j**6 - 2*j**4 + 4/3*j**3 + 7/10*j**5. Factor q(w).
2*(w + 1)*(7*w - 2)**2
Suppose 2*g - 6 = -4*a, -4*a - 6 = -19*g + 17*g. Let o be (a/(-17 + 5))/(-2 - -4). Suppose -27/4*h**4 - 3/2*h**3 + 3/2*h + 27/4*h**2 + o = 0. What is h?
-1, -2/9, 0, 1
Let w(p) be the first derivative of p**4/3 - 56*p**3/9 + 6*p**2 + 432*p - 4952. Factor w(f).
4*(f - 9)**2*(f + 4)/3
Let v(w) = -83*w**2 - 1242*w + 48. Let i be v(-15). Factor -2/5*q**i - 2/5*q**2 + 16/5*q + 24/5.
-2*(q - 3)*(q + 2)**2/5
Let h(l) = l**5 - l**4 - l**3 + l**2 - 2*l. Let n(t) = -6*t**5 + 182*t**4 - 342*t**3 - 10*t**2 + 352*t - 172. Let j(v) = -2*h(v) - n(v). Factor j(x).
4*(x - 43)*(x - 1)**3*(x + 1)
Let z be (-4)/5 - 10387/235. Let d be (-24*5/z)/((-4)/(-6)). Factor -1/8*w**d - 1/4*w**3 + 0 + 7/8*w**2 - 1/2*w.
-w*(w - 1)**2*(w + 4)/8
Let u(n) be the third derivative of 17*n**8/336 + n**7/3 - 37*n**6/40 - 46*n**5/15 - 5*n**4/6 + 842*n**2. Let u(h) = 0. Calculate h.
-5, -1, -2/17, 0, 2
Suppose -6*z = -330 - 102. Solve -61*o**3 + 1 - 30*o + 23*o**3 - 5 + z*o**2 = 0 for o.
-2/19, 1
Let z(h) be the second derivative of -3*h**5/80 - 31*h**4/8 - 112*h**3 + 768*h**2 + h - 156. Factor z(w).
-3*(w - 2)*(w + 32)**2/4
Let s(x) be the second derivative of x**7/14 + x**6/10 - 3*x**5/4 + 3*x**4/4 + 57*x - 7. Solve s(i) = 0.
-3, 0, 1
Let o(l) = 10*l**3 + 26*l**2 - 4*l - 29. Let x(m) = 19*m**3 + 54*m**2 - 9*m - 59. Let f(q) = -5*o(q) + 3*x(q). Suppose f(k) = 0. Calculate k.
-32/7, -1, 1
Let m(a) be the second derivative of -32/5*a**3 - 3/50*a**5 - 73/30*a**4 - 26 - 1/105*a**7 + 3/25*a**6 - 36/5*a**2 - 3*a. Factor m(b).
-2*(b - 6)**2*(b + 1)**3/5
Let z be -6*(-4 - (-39)/9). Let i(k) = 3*k**2 + 2*k + 1. Let f be i(z). Factor 9*y**3 - y**4 + 12*y**4 + f*y**2 - 8*y**4 + 3*y.
3*y*(y + 1)**3
Determine t so that -8/9 - 2/9*t**5 - 2/9*t**4 + 10/9*t**3 - 8/9*t + 10/9*t**2 = 0.
-2, -1, 1, 2
Let j(v) = -v**3 - 7*v**2. Let u(i) = 13*i**3 + 47*i**2 + 1000. Let k(r) = -22*j(r) - 2*u(r). Factor k(t).
-4*(t - 10)**2*(t + 5)
Suppose -467*r - 587 - 2101 = -267*r - 328*r. What is d in -2/3*d**4 + r*d**2 + 13/3*d**3 + 20/3 + 68/3*d = 0?
-2, -1, -1/2, 10
Let h(x) be the first derivative of -x**3 - 17*x**2/2 + 32*x - 195. Let m(b) = 2*b**2 + 19*b - 30. Let g(k) = 3*h(k) + 4*m(k). What is r in g(r) = 0?
1, 24
Let g(i) be the second derivative of 57*i + 17/2*i**4 + 4/15*i**6 + 0 - 31/3*i**3 + 5*i**2 - 29/10*i**5. Suppose g(d) = 0. Calculate d.
1/4, 1, 5
Suppose 6*l - 95 + 167 = 0. Let s be 4 + -6 - ((-18)/l - 5). Determine n, given that n + s*n**2 - n**3 + 0 = 0.
-1/2, 0, 2
Determine i, given that 12544/5 - 448/5*i + 4/5*i**2 = 0.
56
Suppose 7*a + 235 = -73. Let s = a + 46. Factor 4*j**2 + 2*j**3 - s*j**2 + 2*j**4 - 4*j**2 - 2*j.
2*j*(j - 1)*(j + 1)**2
Suppose -5658/7*n - 8003241/7 - 1/7*n**2 = 0. Calculate n.
-2829
Let r(x) = -x**3 - x**2 - x - 48. Let y(t) = 8*t**3 + 11*t**2 + 3*t + 320. Let d(i) = -21*r(i) - 3*y(i). Factor d(u).
-3*(u - 2)*(u + 2)*(u + 4)
Let r(k) = -7*k**4 - 102*k**3 + 213*k**2 - 104*k - 4. Let y(p) = -27*p**4 - 408*p**3 + 852*p**2 - 417*p - 15. Let l(a) = 15*r(a) - 4*y(a). Factor l(v).
3*v*(v - 1)**2*(v + 36)
Determine f so that -2808/7 - 2/7*f**2 - 480/7*f = 0.
-234, -6
Let x = -14801 + 14825. Let i(k) be the first derivative of 1/4*k**3 - 3/16*k**4 + 0*k + 3/4*k**2 + x. Factor i(t).
-3*t*(t - 2)*(t + 1)/4
Let s(k) be the third derivative of -k**8/26880 + 7*k**4/24 + k**3/2 - 5*k**2 - 3*k. Let n(y) be the second derivative of s(y). Solve n(w) = 0.
0
Let f = -16569/31 - -85077/155. Let 24/5*b - 6*b**3 - 18*b**2 + f + 6/5*b**5 + 18/5*b**4 = 0. What is b?
-3, -2, -1, 1, 2
Let i(c) be the third derivative of 0*c**3 + 1/60*c**5 + 0*c + 8*c**2 + 3/8*c**4 - 2. Factor i(l).
l*(l + 9)
Let x be ((-68320)/(-1342) + -51)*11/(-2). Suppose x*w**4 + 11*w**2 - 12*w + 9/2 - 4*w**3 = 0. Calculate w.
1, 3
Let b(y) be the third derivative of 9/8*y**4 + 1/40*y**6 + 2*y**3 + 0 + 0*y - 119*y**2 + 3/10*y**5. Factor b(x).
3*(x + 1)**2*(x + 4)
Factor 190*w - 12*w**3 - 427 + 2*w**4 + 38*w**3 + 527 + 114*w**2 + 0*w.
2*(w + 1)*(w + 2)*(w + 5)**2
Let q = 73/44 - 10/11. Suppose 0 = -8560*f + 8482*f + 234. Solve -9/4*k**2 + 3 + q*k**f + 0*k = 0 for k.
-1, 2
Factor 127/6*w**2 - 2/3*w**3 - 31/6 - 46/3*w.
-(w - 31)*(w - 1)*(4*w + 1)/6
Let 732/5*h**2 + 0 - 448/5*h**4 - 6/5*h**5 - 1142/5*h**3 + 864/5*h = 0. What is h?
-72, -3, -2/3, 0, 1
Let m = 57 + -52. Suppose 49 = m*y - 656. Suppose 5*f**3 - 30*f**2 + 8 + 74*f + 75*f - y*f - f**3 + 10*f**4 = 0. What is f?
-2, -2/5, 1
Solve 200 - 220*m + 12*m**2 - 4/5*m**4 + 44/5*m**3 = 0.
-5, 1, 5, 10
Let p = -1090181/6390 + 3083/18. Let t = p - 5/71. Factor 1/5*u**2 + t + 4/5*u.
(u + 1)*(u + 3)/5
Suppose -20*l**5 + 477*l + 23*l**5 + 1529*l**4 - 1463*l**4 - 372*l**2 - 198 + 42*l - 18*l**3 = 0. Calculate l.
-22, -3, 1
Let q be 27 + 0 + 11/(-11). Suppose 3*k = 2*z + 7*k - q, 3*z - 4 = k. Factor z + 3*l**2 - 15*l**2 + 4*l**3 + 13.
4*(l - 2)**2*(l + 1)
Let t = 500 + -498. Let n(p) = 51*p**2 + 738*p - 831. Let l(a) = 5*a**2 + 74*a - 83. Let k(g) = t*n(g) - 21*l(g). Determine h, given that k(h) = 0.
-27, 1
Let y(b) be the second derivative of 91*b + 1/42*b**4 + 1/105*b**6 + 0*b**3 + 0 + 0*b**2 - 1/35*b**5. Factor y(a).
2*a**2*(a - 1)**2/7
Solve -9/5*x**3 - 3/5*x**4 + 0*x + 0 + 0*x**2 = 0.
-3, 0
Solve 1/6*r**4 - 31/6*r + 5/6*r**2 - 5 + 7/6*r**3 = 0 for r.
-5, -3, -1, 2
Let p(a) be the second derivative of -4*a**6/15 + 42*a**5/5 - 349*a**4/6 - 322*a**3 - 529*a**2 - a - 86. Let p(m) = 0. What is m?
-1, 23/2
Find u such that 152*u - 14*u + 140*u - u**2 + 632 + 118*u - 82*u = 0.
-2, 316
Let c(t) = -t**3 + 125*t**2 + 1634*t + 1373. Let g be c(137). Find z such that 12*z + 94/3*z**2 - 8/3 + 13/3*z**4 + 21*z**g = 0.
-2, -1, 2/13
Let g be ((-17)/2)/(36924/(-1448)). Solve -76/3*k**3 - g*k**5 - 36 - 14/3*k**4 - 81*k - 66*k**2 = 0.
-4, -3, -1
Let v = -577670/3 - -190843. Let m = 1714 + v. Factor -1/