**2 - 8. Let s(h) = -h**5 + 5*h**4 + 4*h**3 - 5*h**2 + 3. Let u(m) = -8*s(m) - 3*z(m). Factor u(o).
-o**2*(o - 2)*(o - 1)*(o + 1)
Let q be -4*1*(-2)/12. Suppose -6 = -2*x - 5*u, 3 = 4*x + 3*u - 9. Determine s, given that 0*s**2 + q*s**x + 0 - 2/3*s = 0.
-1, 0, 1
Let t(m) be the second derivative of -m**7/105 + m**6/20 - m**5/30 - m**4/4 + 2*m**3/3 - 3*m**2/2 - 3*m. Let g(i) be the first derivative of t(i). Factor g(q).
-2*(q - 2)*(q - 1)**2*(q + 1)
Suppose 0 = -2*b - 2*b - 4*b. Let g = 69/4 + -17. Factor 1/2*m**2 + b - g*m - 1/4*m**3.
-m*(m - 1)**2/4
Factor -6 - 4*l - 2/3*l**2.
-2*(l + 3)**2/3
Let c(x) be the first derivative of -1 - 1/4*x - 1/8*x**4 + 1/4*x**5 + 1/2*x**2 - 1/3*x**3 - 1/12*x**6. Determine l so that c(l) = 0.
-1, 1/2, 1
Suppose 3*l - 2*k - 6 = -0, -k - 3 = -2*l. Factor 1/4*p**2 + 0 + l*p.
p**2/4
Suppose 0 = -3*y - 3*g - 15, -g + 2*g = -2*y - 5. Determine v so that -1/4*v**4 + 0*v - 1/4*v**2 + 1/2*v**3 + y = 0.
0, 1
Let a be (-240)/72*12/(-50). Factor 2/5*y + 0 + a*y**2 + 2/5*y**3.
2*y*(y + 1)**2/5
Factor -2/5 - 2/5*h + 2/5*h**3 + 2/5*h**2.
2*(h - 1)*(h + 1)**2/5
Let k = -1 + 3. Factor 6*d + 2*d**3 - d**3 - 12*d**k + 3*d**2 + 2*d**3.
3*d*(d - 2)*(d - 1)
Suppose j + 40 = 5*j. Let f be (12/j)/(2/5). Factor -24/5*r + 12/5*r**2 - 2/5*r**f + 16/5.
-2*(r - 2)**3/5
Suppose -24 + 4*h**2 - 2*h**2 + 9 - 5*h**2 + 18*h = 0. What is h?
1, 5
Let g(x) be the first derivative of 7*x**6/2 - 18*x**5 + 75*x**4/2 - 40*x**3 + 45*x**2/2 - 6*x - 1. Factor g(q).
3*(q - 1)**4*(7*q - 2)
Suppose -85 = -3*c - 22. Let m be c/(-28) - (-58)/56. Factor -2/7*q**2 + 0 - 2/7*q + 2/7*q**4 + m*q**3.
2*q*(q - 1)*(q + 1)**2/7
Let c = -2 + 6. Factor 4*g + 5*g - 7*g + g**c - g**5 - 5*g**2 + 3*g**3.
-g*(g - 1)**3*(g + 2)
Suppose -3*s + p + 5 = 0, -22*s = -25*s + 5*p + 1. Factor -8/3 - 10*x**s - 2/3*x**4 + 14/3*x**3 + 26/3*x.
-2*(x - 4)*(x - 1)**3/3
Let i = 108/7 - 599/42. Let b(a) be the second derivative of -1/5*a**5 + 2*a + i*a**4 - 2/5*a**6 - 1/2*a**3 - a**2 + 0 + 1/6*a**7. Factor b(k).
(k - 1)**3*(k + 1)*(7*k + 2)
Let x = -25 + 33. Let o be (-6)/x*152/(-171). Solve w**5 + 1/3*w - 4/3*w**3 + 0 + o*w**4 - 2/3*w**2 = 0.
-1, 0, 1/3, 1
Let b be 6/21 - 48/(-28). Let a = -2 + 8. Determine z so that -72*z + 0 - a - b - 162*z**2 = 0.
-2/9
Suppose 0 = -3*g - 3*w, -3*g = -0*g - w - 12. Let p(h) be the first derivative of -6*h**2 + 3*h + 7*h**2 + h**g + 1 - 4*h**2. Let p(q) = 0. What is q?
1
Let c(f) be the third derivative of f**7/42 + f**6/8 + f**5/4 + 5*f**4/24 - 8*f**2. Let c(d) = 0. What is d?
-1, 0
Let t(v) = -36*v**2 - 45*v - 30. Let q be (1*3)/((-15)/20). Let r(p) = -7*p**2 - 9*p - 6. Let u(s) = q*t(s) + 21*r(s). Factor u(d).
-3*(d + 1)*(d + 2)
Let u(y) be the second derivative of y**5/20 - y**4/3 + y**3/2 - 15*y. Solve u(b) = 0.
0, 1, 3
Let j(f) = f**2 + f + 1. Let t(c) = -4*c**2 - 4*c - 6. Let h(l) = -6*j(l) - t(l). What is z in h(z) = 0?
-1, 0
Let t = -9 + 12. Let q(b) be the first derivative of -2/25*b**5 - 2 + 2/15*b**t - 1/10*b**4 + 0*b + 1/5*b**2. Find a, given that q(a) = 0.
-1, 0, 1
Factor -20*o - 48*o**2 - 50*o**2 + 8*o + 94*o**2 + 40.
-4*(o - 2)*(o + 5)
Suppose 0*t + 0 + 2/9*t**3 + 0*t**2 = 0. Calculate t.
0
Let u(v) be the third derivative of v**8/1344 + v**7/210 + v**6/80 + v**5/60 + v**4/96 + 12*v**2. Solve u(j) = 0.
-1, 0
Let i(b) = 3*b + 66. Let v be i(-21). Let z(m) be the third derivative of 1/20*m**5 - 3/40*m**6 - 2*m**2 + 0 + 0*m - 2/35*m**7 + 0*m**v + 0*m**4. Factor z(a).
-3*a**2*(a + 1)*(4*a - 1)
Factor 1/3*s**4 + 1 - 2*s**3 + 4*s**2 - 10/3*s.
(s - 3)*(s - 1)**3/3
Let d be 3/((-1)/2*2). Let j be (4 - (-11)/d)*1. Factor 2/3*l**3 - 2/3*l + 0 + 1/3*l**2 - j*l**4.
-l*(l - 2)*(l - 1)*(l + 1)/3
Let g(a) be the third derivative of -a**7/350 + 11*a**6/600 - a**5/20 + 3*a**4/40 - a**3/15 - 4*a**2. Solve g(d) = 0.
2/3, 1
Let x(v) = -v**3 + 10*v**2 - 9*v. Let z be x(9). Factor 0 + z*o - 3/4*o**2.
-3*o**2/4
Let d = -9 - -9. Let u(a) be the second derivative of 0 + 0*a**4 - 1/60*a**6 + 2*a + 0*a**3 + d*a**5 + 0*a**2. Factor u(w).
-w**4/2
Let w(a) = -47*a - 47. Let u be w(-1). Solve 1/5*i**5 - 1/5*i**2 - 1/5*i**3 + u + 1/5*i**4 + 0*i = 0 for i.
-1, 0, 1
Suppose -2*d + 1 = -2*k + 5*k, 3*k = 5*d + 29. Let a be (-1)/d + 21/12. Find c such that c**4 + 2*c**2 + 2*c**2 + c**3 - 3*c**a - 3*c**3 = 0.
0, 1
Let u be 0/(0 - -3) + 3 + 3. Let a(d) be the first derivative of -2*d**4 + 0*d**3 - 2 + 0*d - 1/3*d**u + 8/5*d**5 + 0*d**2. Factor a(r).
-2*r**3*(r - 2)**2
Let h(o) be the third derivative of -o**6/480 - o**5/20 - 3*o**4/8 + 23*o**2. What is g in h(g) = 0?
-6, 0
Let x(i) be the third derivative of -1/60*i**5 + 1/120*i**6 + 0*i - 1/24*i**4 + 0 + 1/6*i**3 + 3*i**2. Factor x(y).
(y - 1)**2*(y + 1)
Let m(l) be the third derivative of -l**8/2520 + l**6/300 - l**5/225 - l**2. Factor m(s).
-2*s**2*(s - 1)**2*(s + 2)/15
Let j(r) be the third derivative of -r**8/8400 - r**7/2100 - r**6/1800 - r**3/6 - 3*r**2. Let l(w) be the first derivative of j(w). Factor l(i).
-i**2*(i + 1)**2/5
Determine i, given that -230*i**4 - 25*i**3 - 196*i**3 - 107*i**3 - 55*i**5 - 160*i**2 + 13*i**3 - 20*i = 0.
-2, -1, -2/11, 0
Let r be 46/(-391) + 464/476. Suppose r*b - 4/7 - 2/7*b**2 = 0. Calculate b.
1, 2
Factor 13*v**3 + 4 - 15*v**2 + v**2 - 19*v**3 + 10*v**4 + 6*v.
2*(v - 1)**2*(v + 1)*(5*v + 2)
Let t = 20 + -16. Factor 1/3*q + q**3 + 0 + q**2 + 1/3*q**t.
q*(q + 1)**3/3
Let k(m) = -m + 1. Suppose 3*f + 4 = 1. Let v be k(f). Find p, given that -p**2 + v*p - p + 3*p + 3*p**2 = 0.
-2, 0
Let i(l) be the first derivative of l**4/3 + 14*l**3/9 + 4*l**2/3 - 8*l/3 + 14. Factor i(d).
2*(d + 2)**2*(2*d - 1)/3
Let c = -444113/5 + 89268. Let y = c - 443. Factor 18/5 - y*d + 2/5*d**2.
2*(d - 3)**2/5
Let d be ((-10)/(-4))/((-5)/(-10)). Let k(a) = -a**2 + 1. Let h(i) = -3*i**2 - i + 2. Let v(w) = d*k(w) - 2*h(w). Factor v(z).
(z + 1)**2
Let a = 33 - 33. Factor -2/9*l + a - 4/9*l**2.
-2*l*(2*l + 1)/9
Factor 377 - 203 - 204 - 10*s**2 - 35*s.
-5*(s + 2)*(2*s + 3)
Let s be 4/6 + (-2)/(-6). Let f(y) = -s - 2*y + 0*y + 3*y. Let g(r) = r**2 - r + 2. Let m(j) = -4*f(j) - 2*g(j). Factor m(z).
-2*z*(z + 1)
Let x(o) be the second derivative of o**4/4 - o**3 + 7*o. Let x(m) = 0. Calculate m.
0, 2
Let m(o) = 9*o**2. Let r be m(1). Suppose -r = -6*f + 3*f. Suppose -6/7*v**f + 0 - 10/7*v**2 - 4/7*v = 0. Calculate v.
-1, -2/3, 0
Let u(y) be the first derivative of -3*y**4/32 + y**3/4 - 3*y**2/16 + 4. What is r in u(r) = 0?
0, 1
Suppose -31 = -5*k + w, 3*k - 15 = 5*w + 8. Let f be 8/k*10/40. Factor 0 - 1/3*d**2 - 2/3*d + f*d**3.
d*(d - 2)*(d + 1)/3
Let y(g) be the third derivative of g**7/70 + g**6/8 + 9*g**5/20 + 7*g**4/8 + g**3 + 8*g**2. Factor y(b).
3*(b + 1)**3*(b + 2)
Let x = -2 - -2. Suppose -8 = -x*i - 2*i. Factor -2*h**2 - 3*h**2 + 6*h**2 - 2*h**3 + h**i.
h**2*(h - 1)**2
Factor -1/5*j**5 + 0*j + 0*j**4 + 1/5*j**3 + 0*j**2 + 0.
-j**3*(j - 1)*(j + 1)/5
Let t(u) be the first derivative of 2*u**5/15 - u**4/6 + 2. Factor t(k).
2*k**3*(k - 1)/3
Suppose -5*s - 15 = -0. Let a = s + 7. Factor -2 - a*y**2 + 2*y + 4 + 0.
-2*(y - 1)*(2*y + 1)
Let h(z) be the second derivative of -z**4/54 + z**3/9 + 4*z**2/9 - 19*z. Factor h(o).
-2*(o - 4)*(o + 1)/9
Let g(o) be the first derivative of 1/180*o**5 - 1 + 0*o**2 + 1/1080*o**6 + 1/72*o**4 + 0*o + 1/3*o**3. Let q(l) be the third derivative of g(l). Factor q(a).
(a + 1)**2/3
Let k(r) be the second derivative of r**4/24 + r**3/6 + r**2/4 - 21*r. Factor k(y).
(y + 1)**2/2
Let v(u) be the third derivative of -4*u**2 + 0 + 0*u**4 + 1/180*u**5 - 1/18*u**3 + 0*u. Factor v(s).
(s - 1)*(s + 1)/3
Factor 29*d**2 + 6*d + 6*d - 31*d**2.
-2*d*(d - 6)
Let c = -1 - -4. Let -2*a**4 + a + 2*a - 2*a**c - 2*a + 2*a**2 + a = 0. Calculate a.
-1, 0, 1
Let n(g) be the third derivative of -g**9/7560 - g**8/840 - g**7/252 - g**6/180 + g**4/8 + 3*g**2. Let p(c) be the second derivative of n(c). Factor p(x).
-2*x*(x + 1)**2*(x + 2)
Let h(r) be the second derivative of r**6/120 + r**5/16 + r**4/8 - r**3/6 - r**2 + 18*r. Factor h(t).
(t - 1)*(t + 2)**3/4
Factor -3 + 2 - 5 + w - 10*w + 3*w**3.
3*(w - 2)*(w + 1)**2
Let a be 1 + 3 - (-1 - -2). Factor d**4 + a*d**2 + d - d**3 - 2*d**4 - 2*d**2.
-d*(d - 1)*(d + 1)**2
Let q(t) be the first derivative of t**3 - 3*t**2/2 - 6*t - 5. Factor q(r).
3*(r - 2)*(r + 1)
Let u(y