(v). Factor z(k).
3*k**2
Let h(y) = y**3 - 10*y**2 + 9*y + 4. Let f be h(9). Suppose s = -2*s + 6. Factor -3*b**4 - 30*b**s - 2 - 4*b**f - 26*b**3 - b**4 - 14*b.
-2*(b + 1)**3*(4*b + 1)
Let f(u) = 12*u**4 - 2*u**3 - 12*u**2 + 2*u. Let s(x) = -25*x**4 + 3*x**3 + 25*x**2 - 3*x. Let b(j) = -5*f(j) - 2*s(j). Factor b(a).
-2*a*(a - 1)*(a + 1)*(5*a - 2)
Let m(j) be the first derivative of 0*j**3 + 3 + 1/4*j**2 + 0*j - 1/8*j**4. Find c, given that m(c) = 0.
-1, 0, 1
Let l(g) = 9*g**4 + 24*g**3 - 90*g**2 + 100*g - 39. Let u(v) = v**4 + v**3 - 1. Let h(o) = -l(o) + 4*u(o). Factor h(r).
-5*(r - 1)**3*(r + 7)
Let d(w) be the second derivative of w**6/30 - w**5/5 + w**4/2 - 2*w**3/3 + w**2/2 + 2*w. Factor d(t).
(t - 1)**4
Determine o so that -3/2*o**3 - 9/2*o**2 - 3/2 - 9/2*o = 0.
-1
Suppose 28 = 2*h + 4*k, k - 4*k + 46 = 4*h. Let r be (-4)/(-8) + 47/h. Factor 8/5*c**5 + 6*c**3 + 0 + 2/5*c + r*c**4 + 14/5*c**2.
2*c*(c + 1)**3*(4*c + 1)/5
Let m(r) be the third derivative of -r**5/210 + r**4/42 - 8*r**2. Find q, given that m(q) = 0.
0, 2
Let h(b) be the first derivative of -b**4/26 + 2*b**3/39 - 6. What is g in h(g) = 0?
0, 1
Factor 4*m**2 - m**4 + 6*m**3 + 3648*m**5 - 3649*m**5 - 8*m - 4 + 4.
-m*(m - 2)*(m - 1)*(m + 2)**2
Let p be (-6)/(-15) + 102/45. Find r such that -8/3 + 2*r**2 - p*r = 0.
-2/3, 2
Let n(d) be the first derivative of 0*d + 0*d**2 + 0*d**4 + 3 - 1/3*d**3 + 1/5*d**5. Factor n(i).
i**2*(i - 1)*(i + 1)
Let i be 5/(-2) - (-2)/(-4). Let v = 4 - i. Let m(u) = 4*u**2 - 8*u + 11. Let j(c) = 2*c**2 - 4*c + 6. Let t(f) = v*j(f) - 4*m(f). Solve t(l) = 0.
1
Factor 3/5*u**4 + 0 + 6/5*u - 6/5*u**3 - 3/5*u**2.
3*u*(u - 2)*(u - 1)*(u + 1)/5
Let c(q) be the third derivative of 0*q + 1/720*q**6 + 2*q**2 + 0*q**3 + 1/180*q**5 + 0 + 0*q**4. Factor c(a).
a**2*(a + 2)/6
Let i = 104 - 102. Let a(m) be the second derivative of -i*m + 1/30*m**6 + 0 + 1/20*m**5 - 1/4*m**4 - 5/6*m**3 - m**2. Let a(r) = 0. What is r?
-1, 2
Let b(q) be the first derivative of -363*q**4/4 - 77*q**3 + 60*q**2 - 12*q - 12. Suppose b(d) = 0. Calculate d.
-1, 2/11
Let c(i) be the first derivative of -2/3*i**3 + 0*i**2 + 2 - 1/2*i**4 + 0*i. What is x in c(x) = 0?
-1, 0
Let q(l) be the third derivative of 1/15*l**5 + 0*l**3 - 1/12*l**4 + 2*l**2 + 0 - 1/60*l**6 + 0*l. Let q(v) = 0. What is v?
0, 1
Suppose 17*m**2 + 4*m**4 - 2*m**3 - 16*m + 4 - 3*m**2 + 10*m**2 - 14*m**3 = 0. What is m?
1
Let w(b) = -5*b**3 + 2*b**2 + 10*b. Let o(x) = 5*x**3 - x**2 - 10*x. Let t(v) = 3*o(v) + 4*w(v). Factor t(i).
-5*i*(i - 2)*(i + 1)
Solve 5*j**3 - 20*j + 76 - 10*j**2 + 1 - 37 = 0 for j.
-2, 2
Let l(h) be the third derivative of -1/9*h**3 + 0*h + 0 + 1/540*h**6 - 1/54*h**5 + 7/108*h**4 - h**2. Factor l(p).
2*(p - 3)*(p - 1)**2/9
Factor -12*s - 74*s**2 + 52*s + 60*s**3 + 2 - 10 - 18*s**4.
-2*(s - 1)**2*(3*s - 2)**2
Let b = -6 + 2. Let z be 2/b*(-20)/30. Factor 1/3*j**2 + 0 + z*j.
j*(j + 1)/3
Let z(r) be the first derivative of r**5/10 + r**4/10 - 2*r**3/15 - 2*r + 2. Let o(f) be the first derivative of z(f). Factor o(b).
2*b*(b + 1)*(5*b - 2)/5
Factor 2*j + 2/3*j**3 + 8/3*j**2 + 0.
2*j*(j + 1)*(j + 3)/3
Let b(d) be the first derivative of -13*d**4/24 + 14*d**3/9 - 17*d**2/12 + d/3 - 41. Suppose b(w) = 0. What is w?
2/13, 1
Let r(x) be the first derivative of x**7/210 + x**6/90 - 7*x**3/3 + 1. Let p(f) be the third derivative of r(f). Find n, given that p(n) = 0.
-1, 0
Let a(g) be the first derivative of -g**9/10584 - g**8/5880 + g**7/2940 + g**6/1260 - g**3 + 2. Let f(m) be the third derivative of a(m). Factor f(h).
-2*h**2*(h - 1)*(h + 1)**2/7
Let m be (-6)/7*(-19 + 12). Determine j, given that -2/5*j**3 - m*j + 14/5*j**2 + 18/5 = 0.
1, 3
Let n(v) be the first derivative of v**4/6 + 2*v**3/3 + 2*v**2/3 - 11. Let n(h) = 0. What is h?
-2, -1, 0
Let n(a) = 2*a**2 + 4*a + 6. Let j(w) = -5*w**2 - 11*w - 18. Let f(k) = -3*j(k) - 8*n(k). Factor f(g).
-(g - 3)*(g + 2)
Factor 2/3*x**2 - 16/3*x + 32/3.
2*(x - 4)**2/3
Factor -z**2 + 0*z**3 + 1/3*z**4 + 2/3*z + 0.
z*(z - 1)**2*(z + 2)/3
Let u be 54/15 + (-8)/(-20). Suppose -n + 2*f = n - 10, -u = 4*f. Find o, given that 1/2*o - o**5 + 1/2*o**3 - 3/2*o**n + 0 + 3/2*o**2 = 0.
-1, -1/2, 0, 1
Suppose -10*a = 9*a. Solve 64/5*s**2 - 8/5*s + a - 162/5*s**4 - 18*s**3 = 0.
-1, 0, 2/9
Suppose o + 30 = -5*q - 2*o, 2*q = -4*o - 26. Let n be q + (9 - 3) - -1. Factor 5/4*u**3 + 0 - 1/2*u**2 + 7/4*u**n + 0*u.
u**2*(u + 1)*(7*u - 2)/4
Let c be (16/9)/(2 + 0). Let q(t) = -t**2 + 16*t + 19. Let o be q(17). Solve -2/9*n**o - c - 8/9*n = 0 for n.
-2
Let y(p) = p**2 + 4*p + 5. Let k be y(-4). Suppose 0*c - k*c + 10 = 0. Suppose 4*q**2 - q**2 + 0*q**2 + c*q = 0. Calculate q.
-2/3, 0
Suppose -8 = -3*l - 2. Factor 0*i**5 - 2*i**4 - 2*i + l*i**2 + 2*i**5 - i**5 + i.
i*(i - 1)**3*(i + 1)
Suppose 0 = -5*y + 8 + 2. Suppose 0 = -y*w - 3*w + 20. Factor 4*d - 6*d + 2*d**2 + w*d.
2*d*(d + 1)
Let w(q) be the second derivative of 1/70*q**5 - 1/105*q**6 - 1/21*q**3 + 0*q**2 + 1/42*q**4 - q + 0. Let w(s) = 0. What is s?
-1, 0, 1
Let i(v) be the first derivative of 2*v**5/75 + v**4/30 - 2*v**3/15 - v**2/15 + 4*v/15 + 29. Solve i(d) = 0.
-2, -1, 1
Let y be ((-112)/(-40))/(4/10). Suppose -o + y - 2 = 0. What is x in 6*x**3 - x - 4*x**3 + 0*x**5 + 4*x**o - 5*x**5 = 0?
-1, 0, 1
Factor -30*f + 5 + 25*f**3 + 60*f**2 - 3*f**4 + 18*f**4 - 75*f**3.
5*(f - 1)**3*(3*f - 1)
Factor -6*i**2 + 5*i**4 + i**4 + 3*i**5 + 58*i - 61*i.
3*i*(i - 1)*(i + 1)**3
Let a(t) = -1 + 8 - 3*t + t + 2*t**2. Let j(n) = -n**2 - n - 1. Let o(u) = -u**2 - 4*u + 4. Let v(b) = 2*j(b) - o(b). Let s(f) = 6*a(f) + 7*v(f). Factor s(i).
i*(5*i + 2)
Let w(n) be the third derivative of n**7/1050 + n**6/300 - n**5/300 - n**4/60 - 2*n**2. Determine o so that w(o) = 0.
-2, -1, 0, 1
Factor -732*n**2 - 160*n**3 - 332*n - 55 + 81*n**4 + 15 - 17*n**4.
4*(n - 5)*(n + 2)*(4*n + 1)**2
Let u be 1*-2*5/(-30). Factor 1/3*o**2 + 0*o - u*o**3 + 0.
-o**2*(o - 1)/3
Suppose -2*s + 19 = 5*l, 4*l + 4*s + 4 - 24 = 0. Let f(d) = -3*d. Let z be f(-1). Suppose 3*v - 2*v**l + 2 + 0*v**z + v**3 = 0. What is v?
-1, 2
Let z(x) = x**2 - 16*x. Let y(n) = -3*n**2 + 33*n. Let m(b) = 6*y(b) + 13*z(b). Factor m(u).
-5*u*(u + 2)
Let u(t) be the second derivative of -1/100*t**5 + 0*t**3 + 0*t**4 + 1/75*t**6 - 1/210*t**7 + 0*t**2 - 4*t + 0. Solve u(n) = 0.
0, 1
Let o be (1 - (-18)/(-15))*-5. Let y be (-2)/(-4)*(o + -1). Factor 1/4*a**2 - 1/4 + y*a.
(a - 1)*(a + 1)/4
Let g(x) be the first derivative of 2*x**5/95 - x**4/38 - 10*x**3/57 - 3*x**2/19 - 20. Find s such that g(s) = 0.
-1, 0, 3
Factor -2/3*d**3 + 8/3 + 0*d - 2*d**2.
-2*(d - 1)*(d + 2)**2/3
Let c = 854/1055 - 2/211. Solve -8/5*h - c*h**3 + 2/15*h**4 + 8/15 + 26/15*h**2 = 0 for h.
1, 2
Let f(q) = -q**4 + q**3 - q**2 + q + 1. Let s(p) = 2*p**5 - 2*p**4 + 3*p**3 - 9*p**2 + 5*p + 6. Let v(z) = -5*f(z) + s(z). Factor v(l).
(l - 1)*(l + 1)**3*(2*l - 1)
Let n(p) = -p**2 + 3*p + 2. Let a be n(3). Factor 2 - 2*s**2 - 3 + s**4 + a.
(s - 1)**2*(s + 1)**2
Suppose -4*p + 5 = 3*z - 0*z, 4*z = -2*p. Suppose 0*n + 2*n - 12 = -4*i, -30 = -4*n - 2*i. Factor -n*w**p + 2*w - w - 4 - 11*w - 2*w**3.
-2*(w + 1)**2*(w + 2)
Let z be (2/(-10))/(6/(-15)). Let c = 2 + 0. Determine q so that q**5 - 3/2*q - c*q**2 - 1/4 + 9/4*q**4 + z*q**3 = 0.
-1, -1/4, 1
Suppose -2*t - 2*t = 0. Suppose -2*w + w - 4*v + 4 = t, 0 = -v. Let -4*h**w + 3*h**3 - 3*h**4 + 0*h**2 - 2*h + 3*h**5 + 3*h**2 = 0. What is h?
-2/3, 0, 1
Let o(a) be the first derivative of 2*a**5/35 - a**4/7 - 8*a**3/21 + 8*a**2/7 - 15. Determine g, given that o(g) = 0.
-2, 0, 2
Let k(n) be the third derivative of -n**8/196 - 19*n**7/735 - n**6/20 - 3*n**5/70 - n**4/84 + 9*n**2. Solve k(v) = 0 for v.
-1, -1/6, 0
Let w(c) = -c**4 - 4*c**3 - 5*c**2 - 2*c + 4. Let d(p) = p**4 + 4*p**3 + 5*p**2 + 2*p - 5. Let y(b) = -4*d(b) - 5*w(b). Factor y(v).
v*(v + 1)**2*(v + 2)
Let b(o) be the second derivative of o**4/108 - 2*o**3/27 + 8*o - 1. Factor b(z).
z*(z - 4)/9
Factor -4/3 - 2/3*b**2 - 2*b.
-2*(b + 1)*(b + 2)/3
Let q be (-24)/(-36) + (-4)/42. Suppose 12/7*h**3 + 0*h - 12/7*h**4 - q*h**2 + 0 + 4/7*h**5 = 0. What is h?
0, 1
Let z be 0*(54/(-156) + 4/(-26)). Find q such that z + 0*q**2 - 3/2*q**3 + 3/2*q = 0.
-1, 0, 1
Suppose 0 = -6*b - 49 + 67. Let 0*c**2 + 1/4*c**4 + 0*c + 1/4*c**5 + 0*c**b + 0 = 0. What is 