**5.
-2*l**3*(l + 1)**2
Suppose 0*k**3 + 4/3*k - 2/3*k**4 + 2*k**2 + 0 = 0. Calculate k.
-1, 0, 2
Suppose 0 = 5*b - 17 - 3. Factor b + 6*l**3 - 90*l**2 - 6*l + 8*l**4 - 2 + 80*l**2.
2*(l - 1)*(l + 1)**2*(4*l - 1)
Let d(m) be the third derivative of m**8/2520 + m**7/1260 + m**3/3 - 4*m**2. Let z(i) be the first derivative of d(i). Factor z(s).
2*s**3*(s + 1)/3
Let n(l) be the first derivative of -l**3/5 - 6*l**2/5 - 9*l/5 - 12. Let n(b) = 0. What is b?
-3, -1
Let i(g) be the first derivative of g**8/5040 - g**7/2520 - g**6/1080 + g**5/360 - 4*g**3/3 + 2. Let w(x) be the third derivative of i(x). Factor w(a).
a*(a - 1)**2*(a + 1)/3
Let t = 3 + -3. Suppose t*q + q = 3. Factor -r**5 - 4*r**2 + q*r**5 - 2*r + 3*r**4 - 4*r**4 + 5*r**4.
2*r*(r - 1)*(r + 1)**3
Let i(h) = -6*h**2 + 30*h - 29. Let l(y) = 3*y**2 - 15*y + 14. Let v(q) = -4*i(q) - 7*l(q). Factor v(p).
3*(p - 3)*(p - 2)
Let y(k) = k**2 + 20*k - 47. Let g(i) = 2*i**2 + 20*i - 46. Let w(j) = -3*g(j) + 4*y(j). Find q such that w(q) = 0.
5
Let n(k) be the third derivative of 0*k**3 + 0*k - 7*k**2 - 1/32*k**4 + 0 + 0*k**5 + 1/160*k**6. Suppose n(t) = 0. What is t?
-1, 0, 1
Let v(y) be the third derivative of -y**8/224 + 3*y**7/140 - 3*y**6/80 + y**5/40 + 8*y**2. Factor v(x).
-3*x**2*(x - 1)**3/2
Let s = 63/94 + -8/47. Determine f so that 1/2*f + 0 + s*f**2 = 0.
-1, 0
Let w = 301 + -887/3. Factor -w*z**4 + 0 + 0*z - 14/3*z**3 - 4/3*z**2 - 2*z**5.
-2*z**2*(z + 1)**2*(3*z + 2)/3
Let o = 174 - 70. Let s = -413/4 + o. Determine r, given that 0 + 0*r - 1/2*r**2 - s*r**4 - 5/4*r**3 = 0.
-1, -2/3, 0
Let m(h) = 5*h**2 + 2*h + 1. Let g be m(-1). Suppose -g*l + 30 = l. Solve -l*b - 2*b**2 - b**5 + b**4 + 1 + 5*b + 0 + 2*b**3 = 0 for b.
-1, 1
Let v = -38 - -77/2. Suppose -1/4 - 1/4*u**4 - 1/4*u**5 + v*u**3 - 1/4*u + 1/2*u**2 = 0. What is u?
-1, 1
Let n = -48 + 19. Let g = n + 30. Factor g - 3*l + 5/4*l**2.
(l - 2)*(5*l - 2)/4
Find z, given that -18*z**4 - 20*z**3 + 20*z - 20 - 14*z**4 + 17*z**4 + 35*z**2 = 0.
-2, -1, 2/3, 1
Let x(p) = -2*p + 1. Let b be x(-1). Let z = b - 1. Suppose 1 + 2*s**2 + 0*s + 2*s**3 - 3*s**z - 2*s = 0. Calculate s.
-1, 1/2, 1
Determine u so that -1/5*u**2 + 4/5*u - 4/5 = 0.
2
Let o(j) be the second derivative of -j**5/270 + j**3/27 - j**2/2 + 2*j. Let g(w) be the first derivative of o(w). Factor g(z).
-2*(z - 1)*(z + 1)/9
Let u be (-15)/9 + 1 + (-140)/(-75). Factor -u*p - 4/5 - 2/5*p**2.
-2*(p + 1)*(p + 2)/5
Let p(a) = -a**5 - 3*a**4 - 2*a**3 + 3*a - 3. Let x(j) = -4*j**5 - 10*j**4 - 6*j**3 - j**2 + 10*j - 10. Let i(r) = 21*p(r) - 6*x(r). What is n in i(n) = 0?
-1, 1
Let l(r) be the first derivative of r**4/3 + 4*r**3 + 10*r**2 - 100*r/3 - 12. Factor l(t).
4*(t - 1)*(t + 5)**2/3
Let h(p) be the second derivative of -p**6/45 + 4*p**5/15 - 8*p**4/9 - 30*p. Let h(j) = 0. Calculate j.
0, 4
Factor -11 - 35*i + 5*i**2 + 35 + 6.
5*(i - 6)*(i - 1)
Let t(q) be the second derivative of -q**4/54 + 2*q**3/9 - q**2 - 9*q. Suppose t(p) = 0. What is p?
3
Let d(n) be the third derivative of 0*n**3 + 1/12*n**4 - 1/20*n**5 - 3*n**2 + 0*n + 0. Factor d(m).
-m*(3*m - 2)
Suppose 2*q = -q + 9. Factor q*g**3 - 5*g**3 + 3*g**3 - 2*g**3.
-g**3
Let s(u) be the third derivative of u**6/540 + u**5/54 + 7*u**4/108 + u**3/9 - 4*u**2. Factor s(f).
2*(f + 1)**2*(f + 3)/9
Let u(l) be the third derivative of -l**8/16800 - l**7/1260 - l**6/225 - l**5/75 + l**4/12 - 2*l**2. Let i(n) be the second derivative of u(n). Factor i(s).
-2*(s + 1)*(s + 2)**2/5
Let x(u) be the first derivative of 4*u**3/3 + 38*u**2 + 72*u + 48. Suppose x(b) = 0. Calculate b.
-18, -1
Let s(v) be the second derivative of -2*v**7/21 + 2*v**6/5 + 2*v**5 + 2*v**4/3 - 6*v**3 - 10*v**2 + 52*v. Solve s(w) = 0.
-1, 1, 5
Suppose -5*m - 17 + 32 = 0. Let p(f) be the third derivative of 0*f + 1/90*f**5 + m*f**2 + 0*f**3 + 1/18*f**4 - 1/180*f**6 + 0. Solve p(n) = 0 for n.
-1, 0, 2
Find v, given that -1/2*v**2 - 1/2*v + 0 = 0.
-1, 0
Factor c**4 + c - 1 - 2*c**2 + 6 + c**5 - 2*c**3 - 4.
(c - 1)**2*(c + 1)**3
Let w be (-9)/6 + (-3)/(-2). Factor f**2 - f + 3 - 5 + 0 + w.
(f - 2)*(f + 1)
Let c = -421 - -421. Determine h, given that -2/13*h**2 + c - 2/13*h**3 + 4/13*h = 0.
-2, 0, 1
Let y(z) = z**2 + 2. Let l be y(0). Let d = 430 - 427. Factor l*w**d + 0 - 4/3*w + 2/3*w**2.
2*w*(w + 1)*(3*w - 2)/3
Let c(b) be the second derivative of -b**5/50 + b**4/30 + b**3/15 - b**2/5 + 8*b. Solve c(g) = 0.
-1, 1
Suppose -2*z + 11 = 5. Suppose d**4 - 2*d**4 - 2*d - 15*d**3 - 5*d**2 - 6*d**3 + 17*d**z = 0. What is d?
-2, -1, 0
Let y = -2/471 + 956/3297. Let -6/7*f**2 + 4/7 + y*f = 0. Calculate f.
-2/3, 1
Let c(v) = v**3 - 7*v**2 + 5*v + 8. Let o be c(6). Find j, given that -1/2*j**o + 1/2 + 1/2*j - 1/2*j**3 = 0.
-1, 1
Let o = 124/135 - 14/27. Let h = -298/5 + 60. Factor 2/5*l - 2/5*l**3 - h*l**2 + o.
-2*(l - 1)*(l + 1)**2/5
Factor -1/3*f**2 - 4/3 + 5/3*f.
-(f - 4)*(f - 1)/3
Let z(j) be the second derivative of -4*j - j**2 - 1/12*j**4 + 0 + 1/2*j**3. Solve z(d) = 0.
1, 2
Factor -5*f + f + 2*f**2 - 2*f + 4*f.
2*f*(f - 1)
Let o be 90/(-150) + (-6)/(-10). Factor -1/2*d**3 + o*d + 0 - d**2.
-d**2*(d + 2)/2
Let y(f) be the first derivative of -4*f**3/15 - 12*f**2/5 - 20. Solve y(w) = 0 for w.
-6, 0
Suppose 11 = 4*m + v - 10, m - 3*v = 15. Suppose h + m = 3*p, -3*p + 4*h = p - 8. Solve -1/2*g**p - 2 - 2*g = 0.
-2
Suppose 0 = 2*t - 0 - 6. Let 16*k**t - 3 - 48*k**2 + 2*k**4 - 4*k**4 - 8 - 21 + 64*k = 0. What is k?
2
Factor -1/3*h**2 - 1/3*h**4 + h**3 - h + 2/3.
-(h - 2)*(h - 1)**2*(h + 1)/3
Suppose 2*c - 6 = -0*c. Let -5*z**3 + 66*z**2 - 9*z**c - 38*z + 6*z**3 + 6 - 10*z**3 = 0. What is z?
1/3, 3
Let a(v) = -v**4 - 4*v**3 + 0*v**4 - 2*v - v**2 - 3 + 0 + 1. Let m(d) = -d**4 - d**3 - d**2 + d + 1. Let t(x) = -a(x) - 2*m(x). Factor t(h).
3*h**2*(h + 1)**2
Let t be -3 + (-4)/6*-12. Find c, given that -7*c + t*c**2 + 4*c**3 + 2*c**5 - 2*c**3 + 3*c - 6*c**4 + c**2 = 0.
-1, 0, 1, 2
Let r(h) be the first derivative of 4*h**3 - 3*h**2/2 + 40. Suppose r(y) = 0. Calculate y.
0, 1/4
Suppose -24 = -5*y + 21. Suppose -3*l - 3 = -y. Factor -3*a**l + 2*a**2 - a**2.
-2*a**2
Factor 4/9*o**5 - 64/9*o**2 + 4/9*o**4 + 64/3 + 128/9*o - 16/3*o**3.
4*(o - 3)*(o - 2)*(o + 2)**3/9
Let s(k) be the first derivative of k**6/60 + k**5/20 + k**4/24 - 7*k + 4. Let n(y) be the first derivative of s(y). Factor n(m).
m**2*(m + 1)**2/2
Let m(d) = d**2 + 6*d + 7. Let x be m(-5). Find n, given that x*n**3 + 5*n + 6*n**2 + 5 + 2*n - n - 3 = 0.
-1
Let y(r) = 2*r**3 + 21*r**2 - 12*r - 9. Let m be y(-11). Find p such that 2/5*p + 0 - 2/5*p**m = 0.
0, 1
Suppose 3*i = -0*i + 9. Suppose 2 - 2*d**2 - i*d**2 + d + 4*d**2 = 0. What is d?
-1, 2
Let o(j) = -2*j + 1. Let v be o(-2). Let y = 8 - v. Solve k**4 + k - 4*k**3 + k + 2*k**y - 1 = 0.
-1, 1
Let f be ((-2)/4)/((-23)/138). Let s(w) be the first derivative of -2/15*w**f - 3/10*w**2 + 2/5*w - 3 + 3/20*w**4. Factor s(i).
(i - 1)*(i + 1)*(3*i - 2)/5
Let o(y) = -8*y**3 - 20*y**2 - 4*y. Let u(d) = -9*d**3 - 21*d**2 - 5*d. Let g(v) = -5*o(v) + 4*u(v). Factor g(z).
4*z**2*(z + 4)
Let t be -2*(-3)/(-48) + 17/72. Let d(n) be the first derivative of 4 - 2/3*n + 1/2*n**2 - t*n**3. Determine s, given that d(s) = 0.
1, 2
Let n(c) be the second derivative of -c**5/5 - 2*c**4/3 - 19*c. Suppose n(w) = 0. Calculate w.
-2, 0
Let v(f) be the first derivative of 2/5*f**2 + 3 - 1/10*f**4 + 2/15*f**3 + 0*f. Factor v(k).
-2*k*(k - 2)*(k + 1)/5
Let r = 11 - 9. Suppose b + 5 = 5*a - 6, r*a = 2*b + 6. Factor -1/2*d - 1/2*d**a + 1.
-(d - 1)*(d + 2)/2
Let c(v) be the second derivative of 0 + 0*v**4 - 1/105*v**6 + 2*v + 0*v**5 + 0*v**3 - 1/147*v**7 + 0*v**2. Factor c(k).
-2*k**4*(k + 1)/7
Let m = -331 + 331. Let s = 335/1548 + 1/172. Solve s*h**2 + m*h - 2/9 = 0.
-1, 1
Let k be 0/8 - 0/(-1)*-1. Let a(i) be the third derivative of 0*i**3 - 1/60*i**5 + k + 0*i - i**2 - 1/24*i**4. Factor a(b).
-b*(b + 1)
Let u(k) be the first derivative of 2*k**5/5 + 3*k**4 + 10*k**3/3 - 24*k**2 - 72*k + 16. Solve u(g) = 0 for g.
-3, -2, 2
Let w be -1 - 2/(10/4 - 3). Factor 0 + 4/3*v - 8/3*v**w + 2*v**4 - 2/3*v**2.
2*v*(v - 1)**2*(3*v + 2)/3
Suppose i**2 - 1/3 + 1/3*i**3 - 2/3*i**4 - 1/3*i = 0. Calculate i.
-1, -1/2, 1
Let n(t) be the third derivative of -1/4*t**4 - 4*t**2 + 5/36*t**6 - 1/6*t**5 + 0*t + 0 - 1/9*t**3. Solve n