**6. Factor u(f).
2*(f + 1)*(f + 2)**2/3
Let l(c) be the first derivative of 3/4*c**2 - 1/6*c**3 - c - 33. Factor l(a).
-(a - 2)*(a - 1)/2
Let q be 1/(-6) - (18848/960 + -20). Let -q*k**5 + 0 - 1/5*k - 6/5*k**3 + 4/5*k**2 + 4/5*k**4 = 0. What is k?
0, 1
Determine q, given that 29*q**2 - 20*q**3 + 5 - 15*q**4 - 20*q**2 + q**2 + 20*q = 0.
-1, -1/3, 1
Let -1186*m**3 + m**2 - m**2 + 1191*m**3 - 20*m = 0. What is m?
-2, 0, 2
Let j(k) be the third derivative of -k**10/75600 + k**8/8400 - k**6/1800 + k**4/6 + 5*k**2. Let t(a) be the second derivative of j(a). Factor t(z).
-2*z*(z - 1)**2*(z + 1)**2/5
Let l(y) be the third derivative of 4*y**7/735 - 97*y**6/420 - 6*y**5/7 - 53*y**4/84 + 26*y**3/21 - y**2 + 3. Find n, given that l(n) = 0.
-1, 1/4, 26
Let t(l) = 3*l - 25. Let o be t(9). Suppose 0 = 2*p - 4*r, -o*p - r - 2*r = -7. Determine d so that -2/7*d**p - 12/7*d - 18/7 = 0.
-3
Let r(w) = w**3 + 12*w**2 - 10*w + 2. Let x be r(-13). Let l = x + 40. Factor -c + 3/4*c**l + c**2 + 0.
c*(c + 2)*(3*c - 2)/4
Let c(i) = -i**2 + 9*i - 9. Let f be c(7). Suppose -f*z + 4*y = -41, z + 0*y - 17 = 3*y. Factor -7*s**4 + z*s**4 + 0*s**4 + 2*s**2.
-2*s**2*(s - 1)*(s + 1)
Let q(j) be the first derivative of j**9/756 - j**8/84 + j**7/70 + j**6/18 - 2*j**5/15 + 2*j**3/3 + 30. Let b(n) be the third derivative of q(n). Factor b(l).
4*l*(l - 4)*(l - 1)**2*(l + 1)
Let f = 7811/4420 + 29/884. Factor f*t + 0 + 3/5*t**2.
3*t*(t + 3)/5
Let u(t) be the third derivative of -t**6/60 - t**5 - 75*t**4/4 - 21*t**2 - t. Determine k so that u(k) = 0.
-15, 0
Let u(s) be the third derivative of -s**7/35 + s**6/60 + s**5/10 - s**4/12 - 3*s**2 + 15*s. Factor u(t).
-2*t*(t - 1)*(t + 1)*(3*t - 1)
Let z(h) be the first derivative of -7/9*h**3 + 0*h - 1/3*h**5 - 1/3*h**2 - 1/18*h**6 - 17 - 3/4*h**4. Factor z(q).
-q*(q + 1)**3*(q + 2)/3
Suppose -5*t + 12 = -13. Factor 84*l + 13*l**t - 40*l**2 - 2*l**5 + 12*l**4 - 38 + 2 - 7*l**5 - 24*l**3.
4*(l - 1)**3*(l + 3)**2
Let i be -17 + ((-6)/5)/(2/(-5)). Let n = -11 - i. Determine r so that -3/4*r**2 + 3/4*r**n + 3/4*r**4 + 0 - 3/4*r = 0.
-1, 0, 1
Let w(l) be the second derivative of l**10/20160 - l**8/4480 + l**4 - 13*l. Let r(k) be the third derivative of w(k). Factor r(z).
3*z**3*(z - 1)*(z + 1)/2
Let u(j) be the third derivative of -j**5/150 + 24*j**4/5 - 6912*j**3/5 + 352*j**2. Factor u(d).
-2*(d - 144)**2/5
Let s = 187481/13 + -14421. Suppose -s*g + 290/13*g**3 + 292/13*g**2 - 16/13 + 72/13*g**4 = 0. What is g?
-2, -1/4, 2/9
Let x(u) be the third derivative of -u**6/360 - 49*u**5/90 - 2401*u**4/72 + 156*u**2. Let x(r) = 0. What is r?
-49, 0
Let z be 17 + 3084/(-180) - 20/(-25). What is i in 4/9*i + 0 + 0*i**3 - z*i**2 + 2/9*i**4 = 0?
-2, 0, 1
Let c(d) = d**2 - d. Let x(i) = i**3 - 4*i**2 - 4*i - 5. Let p(u) = -5*c(u) + x(u). Let j be p(9). Determine a, given that j + 14 + 8*a**2 - 12*a - 6*a**2 = 0.
3
Suppose -90 = 17*b - 90. Let x(q) be the second derivative of -6*q**2 + 1/2*q**4 + 0 + 0*q**3 + b*q**5 - 1/40*q**6 + 8*q. Let x(i) = 0. Calculate i.
-2, 2
Let v be (-1)/((-4)/(-28)) + 9. Suppose -2/3 - 4/3*m - 2/3*m**v = 0. Calculate m.
-1
Let a(w) be the first derivative of w**6/6 - 11*w**5/5 + 19*w**4/4 - 3*w**3 + 715. Suppose a(f) = 0. Calculate f.
0, 1, 9
Let p(j) be the first derivative of j**6/3 + 14*j**5/5 - 21*j**4/2 - 46*j**3/3 + 40*j**2 + 72*j + 26. Let p(r) = 0. Calculate r.
-9, -1, 2
Suppose -634 - 1676 = 14*z. Let x = z - -167. Solve -8/11*n**x + 0*n + 0 - 16/11*n**3 - 6/11*n**4 = 0 for n.
-2, -2/3, 0
Let n = -47 + 53. Suppose -n*t + 0 = -12. Suppose 0*h**4 + 2/11*h - 4/11*h**3 + 0*h**t + 2/11*h**5 + 0 = 0. Calculate h.
-1, 0, 1
Let x(z) be the third derivative of 0*z**3 - 3/80*z**5 + 1/12*z**4 + 0*z + 0 + 1/480*z**6 + 45*z**2. Determine j so that x(j) = 0.
0, 1, 8
Let h(q) be the second derivative of 0 - 4*q + 0*q**3 - 6*q**2 + 1/4*q**4. Factor h(j).
3*(j - 2)*(j + 2)
Factor -1/4*u**5 - u - 13/4*u**3 + 0 - 3/2*u**4 - 3*u**2.
-u*(u + 1)**2*(u + 2)**2/4
Solve -c + 7 - 21 + 10 + c**2 + 4 = 0.
0, 1
Let i be 9 + 3 + -4*1. Let f be ((-4)/i)/(5/(-40)). Factor -10*h - h**3 + f*h - 2*h - 3*h**3 + 12*h**2.
-4*h*(h - 2)*(h - 1)
Let p = 241 - 240. Let k be (6/9)/p + (-124)/(-30). Factor 12/5*c**4 + 2/5*c**5 + 8/5*c + 26/5*c**3 + 0 + k*c**2.
2*c*(c + 1)**2*(c + 2)**2/5
Let q(j) be the first derivative of j**4 - 44*j**3/3 + 68*j**2 - 96*j - 122. Factor q(p).
4*(p - 6)*(p - 4)*(p - 1)
Let m(p) be the third derivative of -p**5/570 + 9*p**4/38 + p**2 + 82. Factor m(x).
-2*x*(x - 54)/19
Let u(l) be the third derivative of l**6/160 + 3*l**5/16 + 63*l**4/32 + 49*l**3/8 + 457*l**2. Factor u(w).
3*(w + 1)*(w + 7)**2/4
Find k such that -4*k**2 - 70/3*k**4 - 62/3*k**3 + 0*k + 0 = 0.
-3/5, -2/7, 0
Let f(c) be the first derivative of 1/2*c**4 + 0*c**5 + 0*c**3 + 0*c - 35 - 1/6*c**6 - 1/2*c**2. Factor f(u).
-u*(u - 1)**2*(u + 1)**2
Let c(g) be the second derivative of -g**6/60 + g**5/15 + g**4/4 + 16*g**2 - 39*g. Let w(b) be the first derivative of c(b). Factor w(h).
-2*h*(h - 3)*(h + 1)
Solve 2/3*s**3 + 26/3*s**2 + 24 + 32*s = 0 for s.
-6, -1
Let c(j) be the third derivative of j**6/120 + 19*j**2. Let b(s) = -2*s**3 + 4*s**2 - 5*s + 2. Let w(l) = -b(l) - c(l). Factor w(v).
(v - 2)*(v - 1)**2
Let t(m) be the second derivative of -1/5*m**5 - 128/3*m**3 - 16/3*m**4 + 0 + 0*m**2 + 15*m. Solve t(h) = 0.
-8, 0
Let f(r) be the second derivative of 21*r + 0 - 1/21*r**4 - 128/7*r**2 - 32/21*r**3. Suppose f(h) = 0. What is h?
-8
Let j be (-1 - -3)*1/2. Let t(d) = -3*d. Let c(a) = -a**2 + 1. Let p(q) = -3*c(q) + t(q). Let o(v) = -1. Let b(w) = j*p(w) - 3*o(w). Factor b(z).
3*z*(z - 1)
Let k be (256/(-112))/(15/(-21)) + -3. Let p(m) be the first derivative of -2/5*m - 2/3*m**3 - k*m**4 - 4/5*m**2 - 6. Solve p(v) = 0.
-1, -1/2
Let s(x) = x**2 - 2*x + 4. Let w be s(4). Let v(z) be the first derivative of 9*z**3 + 8*z + w*z**3 + 19*z + 4*z**3 - 45*z**2 + 7. What is u in v(u) = 0?
3/5
Suppose 3*k + 0*t - 38 = 2*t, -4*k + 3*t = -52. Suppose -12*x = -k*x - 4. Find z such that -1/2*z**3 + 0 - z - 3/2*z**x = 0.
-2, -1, 0
Let z(p) be the second derivative of p**6/540 - p**4/108 - p**2 - 5*p. Let l(b) be the first derivative of z(b). Factor l(f).
2*f*(f - 1)*(f + 1)/9
Let v = 234 - 228. Let i(s) be the third derivative of -1/1176*s**8 + 0*s + 0 + 0*s**3 + 0*s**4 + 0*s**7 + 0*s**5 + 1/420*s**v - 7*s**2. Factor i(o).
-2*o**3*(o - 1)*(o + 1)/7
Factor 0*t - 316/3*t**2 + 0 + 4/3*t**3.
4*t**2*(t - 79)/3
Factor 20/3*o**4 + 0 - 4/3*o**5 - 32/3*o**3 + 0*o + 16/3*o**2.
-4*o**2*(o - 2)**2*(o - 1)/3
Let o = -10 - -15. Factor -4 - o*x**2 + 7*x**2 - 4*x**2 + 6*x.
-2*(x - 2)*(x - 1)
Let f be ((-80)/(-110))/(90/110). Let -2/9*s + 2/3*s**3 - f*s**2 + 4/9 = 0. Calculate s.
-2/3, 1
Suppose 0 = 4*j - 3*j - 8. Let c = j - 7. Factor -2*a**2 + 6*a - a**2 - c - 2.
-3*(a - 1)**2
Let z(p) = 57*p - 1079. Let x be z(19). Let 64/3 + 2156/3*c**3 - 686/3*c**x + 656/3*c + 728*c**2 = 0. What is c?
-2/7, 4
Let l(t) be the third derivative of -t**7/17640 + t**6/2520 + t**5/280 - 11*t**4/6 - 27*t**2. Let q(s) be the second derivative of l(s). Factor q(u).
-(u - 3)*(u + 1)/7
Let j(k) be the second derivative of -4/25*k**5 + 0*k**2 + 13/150*k**6 + 1/15*k**4 - 29*k + 0 + 0*k**3 - 1/70*k**7. Find c such that j(c) = 0.
0, 1/3, 2
Let p(n) be the second derivative of n**5/110 + 95*n**4/22 + 9025*n**3/11 + 857375*n**2/11 - 57*n. Factor p(j).
2*(j + 95)**3/11
Let y be (9/(-6))/(21/(-182)) - -5. Let h(d) be the first derivative of -y*d - 87/2*d**2 - 45*d**3 - 81/4*d**4 - 3*d**5 - 3. Find u, given that h(u) = 0.
-3, -1, -2/5
Let t(q) be the first derivative of -1/4*q - 22 - 1/4*q**2 - 1/12*q**3. Solve t(k) = 0.
-1
Let h = 30058/517 - 2724/47. Factor 0*i + 0 - h*i**3 + 4/11*i**2.
-2*i**2*(i - 2)/11
Let i = -56521/3 + 18841. Suppose -i*s**4 + 0*s + 0 - 2*s**2 + 8/3*s**3 = 0. Calculate s.
0, 1, 3
Let s be (-23 + 30)/((65/(-15) - -2)*-1). Factor -10/7*d + 0 + 3/7*d**2 + 1/7*d**s.
d*(d - 2)*(d + 5)/7
Let n(b) = -5*b - 10. Let i be n(-4). Let t(q) = -q - 1. Let z be t(-3). Let -21*d - 5*d**3 + 6 + 0*d**3 - 4*d**3 + i*d**z + 14*d**2 = 0. What is d?
2/3, 1
Suppose p + 172 - 46 = -16*b, 3*p + 4*b = -26. Factor -3/4*t**p + 3*t - 3/4*t**3 + 3.
-3*(t - 2)*(t + 1)*(t + 2)/4
Find o such that 252/5*o**2 + 2/5*o**4 - 648/5*o - 38/5*o**3 