**8. Factor w(n).
-n**3*(n - 1)*(n + 3)/3
Let j(b) be the first derivative of b**3 - 729*b**2/2 - 1022. What is t in j(t) = 0?
0, 243
Let h(p) = -5*p**2 - 5*p + 6. Let v(q) = -11*q**2 - 11*q + 13. Let z(o) = -9*h(o) + 4*v(o). Let c(m) = m**2 + 27*m - 28. Let d(w) = c(w) - 2*z(w). Factor d(r).
-(r - 24)*(r - 1)
Let x(t) = 19512*t + 97563. Let h be x(-5). Suppose 2/7 - 6/7*m + 6/7*m**2 - 2/7*m**h = 0. What is m?
1
Let x be (-22)/4*-2 - ((-53856)/(-462) - 111). Factor -2/7*i**2 + x + 36/7*i.
-2*(i - 19)*(i + 1)/7
Factor -3/4*f**2 - 513/4 + 45*f.
-3*(f - 57)*(f - 3)/4
Let l be 585/1300 + (-2)/10. Let s(p) be the second derivative of 0 - 1/32*p**4 + 18*p + 0*p**2 + l*p**3. Factor s(z).
-3*z*(z - 4)/8
Let q be (-118)/(-88) + 1668/(-1529). Factor -9 - q*k**2 - 1/8*k**4 - 21/2*k + 9/8*k**3.
-(k - 6)**2*(k + 1)*(k + 2)/8
Let u(f) be the first derivative of -18/7*f**3 - 26/7*f**2 + 114 - 17/7*f - 5/7*f**4 - 1/35*f**5. Factor u(d).
-(d + 1)**3*(d + 17)/7
Let y(r) be the third derivative of 21 - 775/36*r**4 + 2*r**2 + 0*r - 344/63*r**7 - 523/18*r**6 - 1321/36*r**5 - 125/18*r**3 - 20/63*r**8. Factor y(g).
-5*(g + 5)**2*(4*g + 1)**3/3
Suppose -21*u - 698 = -23*u. Let b = u + -1744/5. Factor 1/5 + b*t**2 - 2/5*t.
(t - 1)**2/5
Suppose 0 = 2*w - 2377 + 2373. Let m(p) be the first derivative of 0*p**3 - 3/2*p**4 + 3/2*p**w + 11 + 0*p**5 + 0*p + 1/2*p**6. Factor m(z).
3*z*(z - 1)**2*(z + 1)**2
Factor -2/7*m**3 - 400/7*m - 402/7*m**2 + 0.
-2*m*(m + 1)*(m + 200)/7
Suppose -4*u - g - 5 = -0, 5*u - g - 5 = 0. Determine d, given that -6*d + 17*d + u*d**3 - d**3 - 2*d**2 + d**2 - 9*d**2 = 0.
-11, 0, 1
Let t = -1133153 + 1133155. Suppose 2/5*b**4 + 0*b + 4/5*b**3 + 0 + 0*b**t = 0. Calculate b.
-2, 0
Let k(v) = -v**3 - 37*v**2 + 15*v + 559. Let j be k(-37). Suppose 88*m - 80/3 - 164/3*m**2 + 2*m**3 + 10/3*m**j = 0. What is m?
-5, 2/5, 2
Find h such that 107*h + 180 - 35*h + 27*h - 576 - 19*h - 4*h**2 = 0.
9, 11
Let t(j) be the third derivative of -j**9/3024 - j**8/224 - j**7/168 + 5*j**6/72 - j**4/2 + 27*j**2. Let i(h) be the second derivative of t(h). Factor i(a).
-5*a*(a - 1)*(a + 2)*(a + 5)
Let k(b) = -18*b. Let p(m) = -16*m**2 + 388*m - 1225. Let t(r) = 6*k(r) + p(r). Let t(q) = 0. What is q?
35/4
Let t = -224780/3 - -74927. Determine k, given that -400/3 - t*k**2 - 40/3*k = 0.
-20
Let h(j) = -9*j**3 - 176*j**2 - 491*j - 24. Let o(l) = 26*l**3 + 529*l**2 + 1474*l + 66. Let z(r) = -11*h(r) - 4*o(r). Factor z(w).
-5*w*(w + 3)*(w + 33)
Let q(r) be the third derivative of r**6/420 + 4*r**5/105 - 11*r**4/84 - 6*r**3/7 + 342*r**2 - 1. Factor q(b).
2*(b - 2)*(b + 1)*(b + 9)/7
Let g = 2501 - 2044. Suppose 5*d = g - 447. Solve 36/7*t + 30/7 + 6/7*t**d = 0.
-5, -1
Suppose -36 = -6*j - 2*n, -12*n + 26 = 5*j - 11*n. Factor 2/3*w**3 + 0 + 0*w + 2/3*w**j + 0*w**2.
2*w**3*(w + 1)/3
Suppose 0 = -5*a - 3*j + 47, j - 4 = -0. Suppose -2*g = -3*g + 3*b - 13, 5*b - 23 = g. Factor -7 - 4*n**4 + a + 12*n**g + n**4.
-3*n**2*(n - 2)*(n + 2)
Let u(o) be the first derivative of -o**6/1980 + o**4/33 + o**3/3 + 3*o**2/2 + 67. Let j(c) be the third derivative of u(c). Factor j(f).
-2*(f - 2)*(f + 2)/11
Suppose -2*v - 41 = 5*n - 56, -n + 3 = -2*v. Let p be ((-24)/(-16) - 5/4)*v. What is h in 2/11*h**2 + 4/11*h + p = 0?
-2, 0
Factor 4*r**3 + 35/2 + 1/4*r**5 - 4*r**4 + 77/2*r**2 + 191/4*r.
(r - 14)*(r - 5)*(r + 1)**3/4
Suppose 5*b + 2*n + 11 = 0, 2*b + 3*n + 9 + 2 = 0. Let z be (b/(-7))/((-141)/12 - -12). Find j, given that 3/7*j**3 - z*j - 1/7*j**4 + 0*j**2 + 0 = 0.
-1, 0, 2
Let w = 5437501/7250012 - -2/1812503. Let -7/4*f**2 + w*f**3 + 5/4*f - 1/4 = 0. Calculate f.
1/3, 1
Let w = 169 - 164. Solve w*x**3 + 2*x**4 + 2*x**3 + 2*x**4 + x**3 - 32*x**2 = 0.
-4, 0, 2
Let k(p) = 7*p**2 + 4 + 9*p**2 + 44*p + 16*p**2. Suppose -9 + 0 = 3*l. Let c(v) = 33*v**2 + 44*v + 5. Let r(x) = l*k(x) + 4*c(x). Factor r(n).
4*(n + 1)*(9*n + 2)
Let o(j) be the first derivative of -79/6*j**2 + 32 - 7/9*j**3 - 22/3*j. Factor o(h).
-(h + 11)*(7*h + 2)/3
Let x be ((-4)/10)/(19/90155). Let p = -20870/11 - x. Let p - 2*f**2 + 14/11*f**4 + 24/11*f - 24/11*f**3 = 0. What is f?
-1, -2/7, 1, 2
Let u(f) be the second derivative of 7/6*f**3 + f**2 + 1/10*f**5 - 2*f + 7/12*f**4 + 8. Find d such that u(d) = 0.
-2, -1, -1/2
Let m = -415 + 405. Let o be 21/14*1/((-35)/m). Factor 12/7*x + 9/7 + o*x**2.
3*(x + 1)*(x + 3)/7
Let d(p) be the second derivative of 0 + 0*p**2 - 1/20*p**5 - 41/36*p**4 - 13/9*p**3 + 55*p. Solve d(o) = 0 for o.
-13, -2/3, 0
Let a(n) be the second derivative of -2*n**7/21 + 12*n**6/5 + 376*n**5/5 + 2144*n**4/3 + 3328*n**3 + 8192*n**2 - 7127*n. What is r in a(r) = 0?
-4, -2, 32
Let k(l) be the second derivative of -2/3*l**3 - 4/5*l**2 + 1/5*l**5 + 68*l + 0*l**4 + 4/75*l**6 + 0. Let k(t) = 0. What is t?
-2, -1, -1/2, 1
Let a(w) be the third derivative of 1/672*w**8 - 7*w**2 + 1/35*w**7 + 1/12*w**5 + 7/80*w**6 + 0*w**4 - 1 + 0*w + 0*w**3. Factor a(m).
m**2*(m + 1)**2*(m + 10)/2
Let s be ((-126)/35)/(6/20). Let m be (3/s)/(21/(-112)). Solve m*z + 2 + 2/9*z**2 = 0.
-3
Let t(g) be the second derivative of 1/48*g**4 + 23*g - 5/24*g**3 + 0*g**2 + 0. What is n in t(n) = 0?
0, 5
Let z(d) = -320*d**3 - 1655*d**2 + 2135*d - 90. Let t(j) = -107*j**3 - 551*j**2 + 709*j - 30. Let i(u) = -10*t(u) + 3*z(u). Factor i(n).
5*(n - 1)*(n + 6)*(22*n - 1)
Let u(h) be the first derivative of 4*h**5/5 - 62*h**4 - 256*h**3/3 + 124*h**2 + 252*h - 1368. Factor u(d).
4*(d - 63)*(d - 1)*(d + 1)**2
Determine x, given that 3058/7*x + 24/7*x**4 + 346*x**3 - 612/7 - 8/7*x**5 - 4884/7*x**2 = 0.
-17, 1/2, 1, 18
Let g = 15160 + -15155. Let s(i) be the first derivative of -27/28*i**4 - 54/7*i - 29/7*i**3 - 3/35*i**g + 22 - 117/14*i**2. What is f in s(f) = 0?
-3, -2, -1
Let q = -38 - -38. Suppose -5*u + 235 = 5*z, 0 = -q*z + 2*z - 4*u - 64. Factor -z - n**2 - 20*n + 0*n**2 + 27 - 4*n**2.
-5*(n + 1)*(n + 3)
Let o be (-72)/(-18) - (-17942)/(-5124). Let b = o + 2/1281. Factor 29/2*l**3 + 9*l + 39/2*l**2 + 0 + b*l**5 + 9/2*l**4.
l*(l + 1)*(l + 2)*(l + 3)**2/2
Let v(i) = 7*i**3 + 387*i**2 + 276*i + 445. Let c(p) = p**2 - p - 185. Let h(b) = 6*c(b) + 2*v(b). Factor h(o).
2*(o + 1)*(o + 55)*(7*o - 2)
Let n(x) be the second derivative of -x**5/80 + 17*x**4/48 + x**3 - 27*x**2/2 + 11353*x. Factor n(d).
-(d - 18)*(d - 2)*(d + 3)/4
Let s be (11 + -8)/(6/4). Suppose s*c - 5*t = -9, c - 6*c + 30 = 5*t. Factor -6*w**3 + w**3 - 129*w + 132*w + 2*w**c.
-3*w*(w - 1)*(w + 1)
Let y = 4558 - 4556. Factor 2/3*z**y + 26/3*z - 28/3.
2*(z - 1)*(z + 14)/3
Let v = -70 + 125. Let c = -46 + v. Let -c*o**2 - 9 + 0*o**2 + 13*o**2 - 7 = 0. Calculate o.
-2, 2
Suppose -2*v + 15 - 3 = 0. Suppose 2*o = 4*k - 138, 5*o = -k - 0*o + 7. Find m such that k*m**3 - 31*m**3 + 8*m**2 - v*m**2 = 0.
-2, 0
Let c = -1874 - -1876. Let 6/7*f + 0 + 9/7*f**c + 3/7*f**3 = 0. Calculate f.
-2, -1, 0
Solve -37214*l**2 - 33*l**4 - 49*l**3 - 2*l**5 + 70 - 37181*l**2 - 261*l + 74670*l**2 = 0.
-14, -5, 1/2, 1
Suppose -302024*y = -301950*y - 296. Determine s so that 56*s - 65*s**y - 16 - 25/2*s**5 - 92*s**3 + 8*s**2 = 0.
-2, 2/5
Let j(d) be the first derivative of -4*d**5/5 + 136*d**3/3 - 192*d**2 + 252*d - 246. Factor j(h).
-4*(h - 3)**2*(h - 1)*(h + 7)
Let w(x) be the second derivative of 3*x**5/20 - 111*x**4 - 891*x**3/2 - 669*x**2 - 8*x + 96. Factor w(q).
3*(q - 446)*(q + 1)**2
Let m = -965/49 + 17495/931. Let z = m - -28/19. Determine u so that -2/7*u**4 + z*u**3 + 8/7*u**2 + 0 - 16/7*u = 0.
-2, 0, 2
Let x be (3 - -1)*(-10)/20. Let f(d) = 7*d**2 - 200*d + 2000. Let b(h) = -50*h**2 + 1400*h - 14000. Let p(o) = x*b(o) - 15*f(o). Let p(r) = 0. What is r?
20
Let o = 4660/53 - 88. Let r = o + 664/371. Factor 3/7*i**4 + 9/7*i**2 - r*i - 12/7 + 12/7*i**3.
3*(i - 1)*(i + 1)*(i + 2)**2/7
Let p be 210/75 + 20/(-25). Factor -1/2*r**5 - 13/2*r**3 + 6*r**p + 0 + 3*r**4 - 2*r.
-r*(r - 2)**2*(r - 1)**2/2
Let x(p) be the third derivative of -p**6/30 - 103*p**5/5 - 10609*p**4/2 - 2185454*p**3/3 + 269*p**2 - p. Factor x(u).
-4*(u + 103)**3
Let s(q) = -2*q - 14. Let b be s(-14). Let n be 4 + 310/7 + (-4)/b. Determine y so that -14*y**2 - 27*y**3 - 32 + n*y + 29*y**3 - 7*y**2 + 3*y**2 = 0.
1, 4
Suppose 2*a + 5*i = -488 + 479, -4*a = 5*i + 3. Let l(o) be the first derivative of 5*o**a - 5/6*o**6 - 2 + 0*o + o**5 + 25/4*o**4 