3). Solve 4/9*h**2 + 28/9*h + a = 0.
-6, -1
Let a be (-25)/75 - 26/(-6). Let s(u) be the second derivative of -18*u + 0*u**2 + 1/6*u**a + 0 + 0*u**3 - 1/15*u**6 + 0*u**5. Determine k so that s(k) = 0.
-1, 0, 1
Let l be (-2 + -1)/(15/(-460)). Let c = l + -81. Suppose -1252*d**3 - 2*d**5 + c*d**4 - d**2 + 1235*d**3 - 8 - d**2 + 20*d = 0. What is d?
-1, 1/2, 2
Suppose f - 30 = -5*c - 4*f, -f - 15 = -2*c. Let j be 1/c*(2 - -2). Determine k, given that 0*k - 8/7*k**2 + j + 0*k**3 + 4/7*k**4 = 0.
-1, 1
Suppose -15 + 7 = -2*l. Determine y, given that 8*y**2 - 16 + 1642*y + 0*y**l + 4*y**4 - 16*y**3 + 4 - 1626*y = 0.
-1, 1, 3
Suppose 2*n - 5*v = -19, 2*n = v + 2*v - 9. Suppose -2 - 4 = -n*q. Let -u**q + 6*u**2 - 6*u + 2*u**2 - 5*u**2 = 0. Calculate u.
0, 3
Let a(k) = 44*k**4 + 163*k**3 - 376*k**2 + 88*k - 4. Let j(u) = 10*u**4 + u**3 + u - 1. Let q(i) = -a(i) + 4*j(i). Let q(b) = 0. What is b?
-42, 0, 1/4, 2
Factor 10/9*t**3 - 10816/9 - 116*t**2 + 9152/3*t.
2*(t - 52)**2*(5*t - 2)/9
Let x be (489/252)/((-1)/3) - -5. Let r = x - -171/140. Factor r*b - 2/15*b**2 - 4/15.
-2*(b - 2)*(b - 1)/15
Let m(v) be the second derivative of -v**4/18 - 13*v**3/9 + 38*v**2 + 901*v. Solve m(d) = 0.
-19, 6
Let t(s) = -4416*s + 105987. Let i be t(24). Suppose 12*m + 3/2*m**i + 0 - 9*m**2 = 0. Calculate m.
0, 2, 4
Suppose -3*a = -3 + 39. Let c be a/(-10) + 9/(-45) + 2. Solve 5*w**3 - 12*w**2 - 3*w**3 - 6*w**c - 8*w = 0 for w.
-2, -1, 0
Let j(u) = -u**3 + 16*u**2 - 68*u + 29. Let v be j(14). Let d = 534 + v. Factor 48/5*a**d + 2/5 + 2/5*a**2 - 12/5*a + 32/5*a**4.
2*(a + 1)**2*(4*a - 1)**2/5
Let d(q) be the second derivative of q**6/40 + 21*q**5/16 + 22*q**4 + 96*q**3 + 7416*q. Find n such that d(n) = 0.
-16, -3, 0
Let k be (17/714)/((-8)/14*-10). Let v(m) be the third derivative of -1/480*m**6 + 0*m**3 + 0*m**4 - k*m**5 + 0 + 33*m**2 + 0*m. Factor v(l).
-l**2*(l + 1)/4
Let t(p) = 11*p**3 + 914*p**2 + 43213*p + 82816. Let h(j) = -j**3 + j**2 + 2*j - 1. Let o(s) = -6*h(s) - t(s). Find z such that o(z) = 0.
-91, -2
Let u(r) be the first derivative of -2*r**5/45 - 5*r**4/18 + 82*r**3/27 + 5*r**2 + 2494. Find c, given that u(c) = 0.
-9, -1, 0, 5
Let w(t) = -t**2 - 2186*t + 264615. Let j be w(115). What is a in 3*a**3 + j - 9*a - 66/5*a**2 = 0?
-3/5, 0, 5
Suppose 27 = 15*v - 67 + 19. Let l(f) be the second derivative of -3*f**2 + 5/2*f**4 + 20*f - 3/5*f**v - 4/5*f**6 - 1/2*f**3 + 0 + 5/14*f**7. Solve l(q) = 0.
-1, -2/5, 1
Let w(i) be the first derivative of -i**5 + 55*i**4/2 - 220*i**3 + 180*i**2 + 4320*i + 165. Factor w(l).
-5*(l - 12)*(l - 6)**2*(l + 2)
Find d such that 1/3*d**4 - 6*d**2 + d**3 + 0 - 40/3*d = 0.
-5, -2, 0, 4
Let v be ((-16)/(-10) + -2)/(18/(-90)). Solve 12*r - 14*r**v - 20*r**2 + 32*r**2 = 0 for r.
0, 6
Let g(y) be the second derivative of y**6/3 + 145*y**5/4 + 260*y**4/3 - 1775*y**3/6 + 711*y. Find v, given that g(v) = 0.
-71, -5/2, 0, 1
Suppose -131 = 13*f - 13638. Let l = -1037 + f. Factor -2/3*u**3 + 0*u**l + 2*u - 4/3.
-2*(u - 1)**2*(u + 2)/3
Let z = 104145/4844 - -1/4844. Find l, given that -2*l**2 + 11/2 + z*l = 0.
-1/4, 11
Let u(v) be the second derivative of v**4/22 - 116*v**3/11 + 684*v**2/11 - 5759*v. What is o in u(o) = 0?
2, 114
Let i(r) be the first derivative of -185 + 19/7*r**2 + 2/21*r**3 - 40/7*r. Factor i(q).
2*(q - 1)*(q + 20)/7
Let k(w) be the second derivative of 11*w**5/5 - 163*w**4/3 + 248*w**3/3 + 56*w**2 - 95*w - 4. Solve k(h) = 0 for h.
-2/11, 1, 14
Let q(n) = -n**3 + 36*n**2 - 129*n + 9. Let f(m) = 36*m**2 - 128*m + 6. Let o(j) = 3*f(j) - 2*q(j). Factor o(u).
2*u*(u - 3)*(u + 21)
Let j = 2193 + -2190. Let x(s) be the second derivative of 20*s + 2*s**2 + 0 + 1/3*s**4 + 4/3*s**j. Solve x(n) = 0.
-1
Let i(z) = -z**3 - 11*z**2 + 26*z + 2. Let l be i(-13). Find g such that 25*g + 22*g - 2*g - g**2 + 35*g + 3*g**l = 0.
-40, 0
Let k(r) be the first derivative of 3*r**3 + 12*r**2 + 72*r + 262. Let z(g) = 6*g**2 + 12*g + 36. Let t(f) = 3*k(f) - 5*z(f). Solve t(u) = 0.
-2, 6
Let c(g) be the first derivative of 0*g + 97 - 1/6*g**3 - 3/4*g**2. Factor c(q).
-q*(q + 3)/2
Let t(r) = r**3 - 10*r**2 + 13*r + 31. Let a be t(8). Solve n**2 - 71 - 14*n**3 + 0*n**2 - n**5 - 3*n**2 + 9*n**4 - a*n + 22*n + 64 = 0 for n.
-1, 1, 7
Let h = 500410 - 500410. What is t in h*t + 3/7*t**2 - 3/7 = 0?
-1, 1
Let k(w) be the third derivative of 53/6*w**4 + 0*w + 4*w**3 - 2 - 15*w**2 - 38/15*w**5. Factor k(o).
-4*(2*o - 3)*(19*o + 2)
Let n(h) = h**3 + 2*h**2 - h - 2. Let y(q) = -5*q - 51. Let v be y(-10). Let a be n(v). Factor 4/3*g**2 + 4/3*g + a + 1/3*g**3.
g*(g + 2)**2/3
Let c(x) = -1. Let g(n) = -5*n**3 + 5*n**2 + 20*n - 18. Let r be (-20)/35 - 9/21. Let l(z) = r*g(z) - 2*c(z). Factor l(q).
5*(q - 2)*(q - 1)*(q + 2)
Let n = 53/362 + 353/2534. Suppose 2/7*w**3 + 2/7*w**2 - n*w**4 + 0 + 0*w - 2/7*w**5 = 0. What is w?
-1, 0, 1
Let i(v) be the first derivative of -v**6/72 - v**5/6 - 11*v**3/3 + 4. Let x(j) be the third derivative of i(j). Factor x(f).
-5*f*(f + 4)
Suppose 0 = -i + 2*g + 35, 15*g = -i + 11*g + 17. Determine z so that 99*z**3 + i*z**2 + 3*z - 31*z**2 - 42*z**4 - 105*z**3 + 3*z**5 + 86*z**2 - 42 = 0.
-1, 1, 14
Factor 120/11 - 1/11*p**3 + 139/11*p + 18/11*p**2.
-(p - 24)*(p + 1)*(p + 5)/11
Let m = -305 + 308. Factor -a + 5 + 9*a - 6*a**2 + a**3 - 10 + m*a - 1.
(a - 3)*(a - 2)*(a - 1)
Let h be (680/(-476) - ((-11)/(-7) - 3))/(-2). Factor h*w - 6/7*w**5 + 0*w**2 - 6/7*w**3 + 12/7*w**4 + 0.
-6*w**3*(w - 1)**2/7
Suppose 0 = -5*v + i - 132, 0 = -5*v + 2*i - 7*i - 150. Let m be (8/3)/((-324)/v). Suppose -2/3 + 4/9*u + m*u**2 = 0. What is u?
-3, 1
Let o(t) be the first derivative of 135/4*t**4 - 30*t**2 - 57 - 27/2*t**6 + 24*t - 10*t**3 + 0*t**5. Factor o(n).
-3*(n + 1)**2*(3*n - 2)**3
Let v(g) = -g**3 + 6*g**2 - 2*g - 19. Let k be v(5). Let d = k + 6. Factor 0 + 1/4*l**d - 1/4*l.
l*(l - 1)/4
Let o(p) be the second derivative of 2/3*p**4 + 0 - 10/3*p**3 - 6*p**2 + 2/15*p**6 + 6/5*p**5 - 2/21*p**7 - 46*p. Factor o(f).
-4*(f - 3)*(f - 1)*(f + 1)**3
Let i = -1652 + 765. Let u = -887 - i. Factor -1/3*q - 1/3*q**3 - 2/3*q**2 + u.
-q*(q + 1)**2/3
Let m(p) be the second derivative of -p**5/20 - 35*p**4/3 + 191*p**3/2 - 216*p**2 - 3158*p. Factor m(k).
-(k - 3)*(k - 1)*(k + 144)
Factor -232/13 + 2/13*g**2 + 50/13*g.
2*(g - 4)*(g + 29)/13
Let f(d) be the third derivative of d**6/200 - 11*d**5/50 + 13*d**4/8 + 338*d**3/5 - d**2 + 865. Let f(b) = 0. Calculate b.
-4, 13
Let d(c) be the second derivative of c**7/14 + 3*c**6/5 - 441*c**5/20 + 67*c**4 + 498*c**3 + 864*c**2 + 2*c + 789. Let d(f) = 0. Calculate f.
-16, -1, 6
Let a(w) be the third derivative of 9/35*w**7 - w**2 + 1/3*w**3 + 6*w + 0 + 8/5*w**5 + 27/20*w**6 + 23/24*w**4 - 27/112*w**8. Solve a(c) = 0.
-1/3, 2
Suppose 2063 = 2*w + 3*x, 4*x = 3*w - 1497 - 1572. Let j = 3089/3 - w. Factor -j*o + 8 + 2/9*o**2.
2*(o - 6)**2/9
Solve 50/3*v**2 - 10/3*v**3 + 5/3*v - 25/3 + 5/3*v**5 - 25/3*v**4 = 0 for v.
-1, 1, 5
Let d(k) be the third derivative of k**7/840 + k**6/480 - k**5/48 + k**4/32 + 858*k**2. Solve d(z) = 0 for z.
-3, 0, 1
Let d(r) = 19*r**3 + 164*r**2 - 237*r + 108. Let b(m) = -39*m**3 - 329*m**2 + 473*m - 210. Let p(v) = 6*b(v) + 11*d(v). Factor p(x).
-(x + 8)*(5*x - 3)**2
Solve 1790 + 1001*m + 1493 + 257 - 89*m**2 + 759*m + 84*m**2 = 0 for m.
-2, 354
Let v(r) be the third derivative of -r**5/60 - 55*r**4/24 - 125*r**3/3 + 155*r**2 + 1. Solve v(a) = 0 for a.
-50, -5
Let x(n) = n**3 + 163*n**2 + 4292*n + 70. Let p be x(-33). Factor 6*o**2 + 0 - 3/8*o**p + 9/4*o**3 + 0*o.
-3*o**2*(o - 8)*(o + 2)/8
Solve -25*c**4 - 90304*c + 132 - 3*c**5 + 7*c**4 + 90151*c - 114*c**2 + 156*c**3 = 0.
-11, -1, 1, 4
Let s = 11791 - 35371/3. Let c(n) be the first derivative of s*n - 1/12*n**4 + 1/15*n**5 + 2 - 1/3*n**3 + 1/6*n**2. What is i in c(i) = 0?
-1, 1, 2
Let n(k) be the first derivative of -4/7*k**2 + 0*k + 77 + 1/2*k**4 - 8/7*k**3. Determine j, given that n(j) = 0.
-2/7, 0, 2
Let r be 21648/(-105) + 43/(-43). Let z = r - -1038/5. Factor 12/7*f + z*f**2 + 9/7.
3*(f + 1)*(f + 3)/7
Let z be (0/(1269/(-27)))/(12 - 5). Factor z - 3*w**2 + 3/7*w**4 + 0*w**3 + 18/7*w.
3*w*(w - 2)*(w - 1)*(w + 3)/7
Let r(k) be the second derivative of -k**4/54 + 242*k**3/9 - 14641*k**2 + 4*k + 38. What is y in r(y) = 0?
363
Let j(y) be the third deri