8. Let k(c) = 7*c**4 + c**3 + 2*c**2 - 34*c - 15. Suppose -27 = 10*r - 7*r. Let l(s) = r*p(s) + 4*k(s). Factor l(d).
(d - 4)*(d - 3)*(d + 1)**2
Let z(u) be the second derivative of -3*u**2 + 7/3*u**3 - 3/5*u**5 - 1/3*u**4 - 1/21*u**7 - 4 + u + 1/3*u**6. Factor z(r).
-2*(r - 3)*(r - 1)**3*(r + 1)
Let s(b) be the third derivative of b**5/360 - 449*b**4/72 + 201601*b**3/36 + 5*b**2 - 2*b - 5. Factor s(k).
(k - 449)**2/6
Let q(r) be the second derivative of -r**8/1680 + r**7/210 + r**6/180 - r**5/10 - 17*r**4/6 + 12*r + 3. Let z(j) be the third derivative of q(j). Factor z(w).
-4*(w - 3)*(w - 1)*(w + 1)
Let h = -887824/5 - -177575. Solve 57/5*s**2 - 9/5*s**5 - 42/5*s - 57/5*s**4 + h*s**3 + 0 = 0.
-7, -1, 0, 2/3, 1
Factor -100542*a - 4*a**3 - 56443 + 2290*a**2 - 190891 - 39962 - 150*a**2 - 184610*a.
-4*(a - 268)**2*(a + 1)
Determine i so that 7*i**5 - 145*i**3 + 17*i**4 + 41*i**4 - 256*i**2 - 3663205*i + 3663145*i = 0.
-10, -1, -2/7, 0, 3
Let a = 4566/37 + -8281/74. Find q, given that -a*q + 73/4*q**3 + 39/4*q**2 + 2 - 5*q**4 = 0.
-1, 1/4, 2/5, 4
Find g such that -16*g + 1 + 92*g + 4*g + 5 + 98*g**2 + 24*g = 0.
-1, -3/49
Let b(g) be the second derivative of -g**5/300 - 71*g**4/60 - 5041*g**3/30 + 105*g**2 - 8*g + 18. Let s(u) be the first derivative of b(u). Factor s(x).
-(x + 71)**2/5
Let h(z) be the third derivative of 28 + 0*z + 1/40*z**6 - 17/20*z**5 + 10*z**4 - 32*z**3 - 2*z**2. Factor h(p).
3*(p - 8)**2*(p - 1)
Let c(w) be the first derivative of 5/6*w**4 + 5/2*w**2 + 4/3*w**3 + 1/30*w**6 + 4/15*w**5 + 22 + 0*w. Let y(m) be the second derivative of c(m). Factor y(q).
4*(q + 1)**2*(q + 2)
Solve -64/7*x + 0 + 2/7*x**2 = 0 for x.
0, 32
Let t(n) be the first derivative of 25*n**6/6 - 158*n**5 + 215*n**4/2 + 1100*n**3/3 - 455*n**2/2 - 310*n + 950. What is w in t(w) = 0?
-1, -2/5, 1, 31
Let 1587 + 300*r**2 + 1348*r - 2116*r + 1425*r + 723*r = 0. What is r?
-23/10
Let c = -51 + 55. Factor 6*t**2 - 2*t**5 - 12*t**2 - 12 + 26*t - 24*t**3 + 16*t**c + 2*t**2.
-2*(t - 6)*(t - 1)**3*(t + 1)
Solve 844*i - 55*i + 1240 + 499 + 466 - 63*i - 3*i**2 = 0 for i.
-3, 245
Let r(l) be the second derivative of -l + 3/4*l**2 + 1/80*l**5 + 11/24*l**3 + 1/8*l**4 + 42. Let r(g) = 0. Calculate g.
-3, -2, -1
Let c(j) = 3*j**4 - 37*j**3 + 45*j**2 - 31*j - 5. Let z(d) = -6*d**4 + 72*d**3 - 90*d**2 + 60*d + 9. Let x(p) = 9*c(p) + 5*z(p). Factor x(b).
-3*b*(b - 7)*(b - 1)**2
Let y be ((-13)/(-624))/((-67)/(-1206)). Let s = -1/18 - -31/72. Solve -y - 3/8*f + 3/8*f**2 + s*f**3 = 0.
-1, 1
Let k(j) = 31*j**2 - 52*j - 13. Let a(o) = 8*o**2 - 13*o - 3. Let b = 189 + -167. Let z(g) = b*a(g) - 6*k(g). Factor z(y).
-2*(y - 3)*(5*y + 2)
Let m = 5733865/9 - 637081. Let -2/9 - 134/9*v + m*v**2 = 0. Calculate v.
-1/68, 1
Let a(v) be the first derivative of -2/9*v**3 + 0*v**4 + 1/3*v + 1/15*v**5 + 0*v**2 - 5. Factor a(u).
(u - 1)**2*(u + 1)**2/3
Let g = 235 + -209. Suppose 0 = -10*n + g*n - 48. Let 4*b**2 - 7/3*b**n - 2/3 - b = 0. What is b?
-2/7, 1
Let u(d) be the second derivative of 3*d**5/20 - 9*d**4/2 + 65*d**3/2 + 126*d**2 - d - 120. Find m such that u(m) = 0.
-1, 7, 12
Let j(n) be the second derivative of -3*n**5/5 + 47*n**4/4 - 34*n**3 - 30*n**2 - 1532*n. Solve j(v) = 0 for v.
-1/4, 2, 10
Suppose -102/11*j**3 + 0 - 2/11*j**5 + 38/11*j**4 + 98/11*j**2 - 32/11*j = 0. Calculate j.
0, 1, 16
Let g(m) be the second derivative of 4*m**4 + 110*m**3/3 + 56*m**2 + 367*m. Factor g(l).
4*(l + 4)*(12*l + 7)
Let i(a) = 78*a**2 - 1060*a + 168. Let h(g) = -26*g**2 + 352*g - 56. Let z(q) = -11*h(q) - 4*i(q). Find c, given that z(c) = 0.
2/13, 14
Suppose -158*d + 161*d - 3*t = -18, 0 = -3*d - t + 6. Let i(z) be the second derivative of 7/6*z**4 + d - 8/3*z**3 + 3*z**2 - 1/5*z**5 + 15*z. Factor i(j).
-2*(j - 1)**2*(2*j - 3)
Let s(m) = -9*m**2 + 106*m + 2. Let n(p) = 36*p**2 - 429*p - 9. Let o(z) = -2*n(z) - 9*s(z). Determine f, given that o(f) = 0.
0, 32/3
Let m = 17836 + -17833. Let k(d) be the third derivative of 0*d**m + 0 + 0*d**5 + 0*d + 1/30*d**6 - 1/105*d**7 - 23*d**2 + 0*d**4. Factor k(f).
-2*f**3*(f - 2)
Let c = -2373 + 2373. Let k(q) be the third derivative of -1/6*q**3 + 0 + 1/960*q**6 + 18*q**2 - 1/480*q**5 + c*q - 5/96*q**4. Find i, given that k(i) = 0.
-2, -1, 4
Let r(g) = -50*g**3 + 54*g**2 + 249*g + 210. Let z(c) = -23*c**3 + 27*c**2 + 125*c + 105. Let u(s) = 6*r(s) - 13*z(s). Solve u(n) = 0 for n.
-21, -5, -1
Let c be ((-235)/(-990))/1 + 4/(-22). Let t(f) be the second derivative of c*f**3 - 1/18*f**4 - 1/60*f**5 + 0 + 1/3*f**2 + 18*f. Factor t(l).
-(l - 1)*(l + 1)*(l + 2)/3
Let r(z) = 8*z**2 - 15*z - 32. Let m(d) = 13*d**2 - 31*d - 64. Let p(y) = 3*m(y) - 5*r(y). Factor p(u).
-(u + 2)*(u + 16)
Let j be (-268)/(-16) - 2 - (-1)/4. Suppose 6*c - 3*c - 7 = -a, j = 3*c - 3*a. Factor -4*v + c*v**2 - v**2 + 2 + 1 - 1.
2*(v - 1)**2
Let k be -1*(-24)/(-5)*(18 - (588/48 - -7)). Let 22/7*v**2 - 62/7*v - 2/7*v**3 + k = 0. Calculate v.
1, 3, 7
Let n(h) = -215*h**2 - 866*h + 62. Let y be n(-4). Determine g so that -1/2*g**5 + 10*g**4 - 97/2*g**3 + 28 + 97*g**2 - y*g = 0.
1, 2, 14
Let k be ((-5852)/(-3762))/((-7)/(-8)). Factor 8/3 + 2/9*q**2 + k*q.
2*(q + 2)*(q + 6)/9
Let x be (44/(-14))/(35 - 36) + 10/(-7). Factor 3/7*t**2 - 9/7*t - x.
3*(t - 4)*(t + 1)/7
Suppose -3*m - 1 = 8. Let c(z) = 6*z - 660 - 8*z**2 + 6*z + 680. Let u(s) = -9*s**2 + 13*s + 19. Let d(o) = m*c(o) + 4*u(o). Determine k, given that d(k) = 0.
-2/3, 2
Let q(i) = 8*i**3 + 14*i**2 + 16*i - 2. Let u(s) = -90 + 42*s**2 - 13*s + 44 + 23*s**3 + 62*s + 42. Let f(l) = -17*q(l) + 6*u(l). Factor f(k).
2*(k + 1)**2*(k + 5)
Let j(b) be the third derivative of -11/21*b**3 + 0*b + 1/420*b**6 + 11/210*b**5 + 1 + 22*b**2 - 1/84*b**4. Suppose j(w) = 0. What is w?
-11, -1, 1
Let w(v) be the first derivative of -v**7/70 - v**6/40 + 3*v**5/10 + v**4/2 - 4*v**3 - 172*v**2 + 130. Let d(m) be the second derivative of w(m). Factor d(z).
-3*(z - 2)*(z - 1)*(z + 2)**2
Let l(n) be the second derivative of 0*n**4 + 0 + 0*n**3 - 2/5*n**5 + 6*n + 1/5*n**6 + 0*n**2 + 1/21*n**7. What is a in l(a) = 0?
-4, 0, 1
Let u(c) be the second derivative of c**5/20 + 17*c**4/4 + 104*c**3 - 338*c**2 + 3*c - 139. Solve u(d) = 0 for d.
-26, 1
Let x(c) be the second derivative of c**7/2100 + c**6/225 - c**5/60 + 61*c**3/3 + 322*c. Let y(f) be the second derivative of x(f). Solve y(v) = 0 for v.
-5, 0, 1
Suppose 632*t - 176*t**2 + 378*t**2 - 198*t**2 + 456*t - 4416 = 0. Calculate t.
-276, 4
Suppose 2*a = -10*a - 4*h + 16, 3*a = 2*h + 19. Factor 4/3*m**2 + 4/9*m + 4/3*m**a + 4/9*m**4 + 0.
4*m*(m + 1)**3/9
Determine w, given that 690*w**2 + 23/3*w**4 + 1/6*w**5 + 709/6*w**3 + 0 + 1350*w = 0.
-18, -5, 0
Suppose -5*w + 23 = -37. Let d = -684 + 773. Factor -d*t + 105*t - w*t**2 - 8*t**3 + 4*t**3.
-4*t*(t - 1)*(t + 4)
Let v(l) be the third derivative of 1/144*l**4 + 7*l - 5*l**2 + 0*l**3 + 1/180*l**5 + 0 + 1/720*l**6. Determine f, given that v(f) = 0.
-1, 0
Let k(x) be the third derivative of x**6/540 - x**4/9 - 40*x**3 - 38*x**2. Let n(p) be the first derivative of k(p). Factor n(z).
2*(z - 2)*(z + 2)/3
Let k(b) = 512*b**4 - 100*b**3 - 468*b**2 + 28. Let z(q) = -93*q**4 + 18*q**3 + 85*q**2 - 5. Let g(t) = 5*k(t) + 28*z(t). Let g(c) = 0. What is c?
-10/11, 0, 1
Let c = -50419 + 100843/2. What is s in -c*s + 1/2*s**4 + 5/2*s**3 + 3/2*s**2 - 2 = 0?
-4, -1, 1
Solve 162/5 + 12*b**3 - 6*b**4 + 76*b**2 + 2/5*b**5 + 90*b = 0 for b.
-1, 9
Suppose 0 = -1889*y + 1821*y. Factor y + 3/4*o**2 - 15/4*o.
3*o*(o - 5)/4
Let v(z) = z**2 - 43*z + 56. Suppose -30*w = 286 - 76. Let y(c) = c**2 - 29*c + 38. Let i(t) = w*y(t) + 5*v(t). Factor i(g).
-2*(g - 1)*(g + 7)
Factor 0 - 78*t - 171/4*t**2 + 15/4*t**3.
3*t*(t - 13)*(5*t + 8)/4
Let n(y) be the first derivative of -44/3*y**3 + 1 - 4/5*y**5 - 6*y**4 - 12*y**2 + 0*y. Solve n(b) = 0.
-3, -2, -1, 0
Factor 34*u + 174*u + 38*u**2 + 35 + 0*u**2 + 55.
2*(u + 5)*(19*u + 9)
Let i(p) be the first derivative of -p**3/21 + 27*p**2/7 + 61*p - 3717. Solve i(v) = 0 for v.
-7, 61
Let s(g) = -38*g**2 - 997*g - 81619. Let u(x) = 11*x**2 + 332*x + 27209. Let q(k) = -4*s(k) - 14*u(k). What is z in q(z) = 0?
-165
Let z(y) be the first derivative of 5*y**6/6 + 26*y**5 - 215*y**4/2 + 160*y**3/3 + 425*y**2/2 - 290*y - 4625. Solve z(i) = 0 for i.
-29, -1, 1, 2
Let q(c) be