75. Factor 6*a**2 - 28*a**3 - 36 - 3*a**z + 55*a**3 + 18*a - 30*a**3 + 6*a.
-3*(a - 2)**2*(a + 3)
Suppose 499*x = 491*x + 32. Let o(d) = -5*d**3 + 23*d**2 + 36*d + 12. Let g(i) = -i**3 - 2*i**2 - i. Let a(w) = x*g(w) + o(w). Factor a(k).
-(k - 3)*(3*k + 2)**2
Let q(y) = 5*y**3 - 67*y**2 + 113*y - 59. Let d(n) = 2*n**3 - 4*n**2 - n - 1. Let l(v) = 10*d(v) - 5*q(v). Let l(r) = 0. Calculate r.
1, 57
Let m(z) be the second derivative of z**7/42 + 23*z**6/15 - z**5/20 - 23*z**4/6 + 1073*z. Factor m(v).
v**2*(v - 1)*(v + 1)*(v + 46)
Suppose -228 = -12*u + 732. Solve 61 + u - 2*l + 2*l**2 - 141 = 0 for l.
0, 1
Let g be -1*(-36)/45 - (-9)/(45/10). Let t(j) be the first derivative of -3*j**2 - g*j**5 + 51/10*j**4 - 4/5*j - 18 + 2/15*j**3. Solve t(p) = 0 for p.
-2/5, -1/7, 1
Suppose 0 = 2*f + 1 - 15. Let a be (-124)/(-14) + 0 + 2/f. Factor 100/7*r**3 - a*r**4 + 4*r - 4/7 - 76/7*r**2 + 16/7*r**5.
4*(r - 1)**3*(2*r - 1)**2/7
Find h, given that 25*h**4 + 19*h**4 - 1600*h + 353*h**2 + 367*h**2 + 48*h**3 - 48*h**4 = 0.
-10, 0, 2, 20
Suppose -2*m = -2*r + 10, -848*r + 846*r + 10 = -3*m. Let 2/5*q**3 + 4/5*q**2 - 4/5*q**4 - 2/5*q**5 + 0 + m*q = 0. What is q?
-2, -1, 0, 1
Let n(k) be the first derivative of k**3/2 + 51*k**2/4 + 63*k + 1772. Factor n(g).
3*(g + 3)*(g + 14)/2
Let a(h) be the third derivative of -5/42*h**4 - 38*h**2 + 11/21*h**3 + 0 + 0*h - 1/210*h**5. Factor a(p).
-2*(p - 1)*(p + 11)/7
Let y be 3*(-35)/(-15) - (-1 + 1) - 7. Let n(p) be the third derivative of y + 5/3*p**3 + 0*p - 29*p**2 + 1/60*p**5 + 7/24*p**4. Factor n(x).
(x + 2)*(x + 5)
Let p = 12793/668 - -233/668. Factor -p*t**3 + 0 - 54*t - 72*t**2 - 3/2*t**4.
-3*t*(t + 1)*(t + 6)**2/2
Let q(c) be the second derivative of 2/15*c**6 - c**4 + 0*c**2 + 0*c**5 + 3 - 5*c - 4/3*c**3. Factor q(t).
4*t*(t - 2)*(t + 1)**2
Let k(m) be the first derivative of -m**4/10 - 388*m**3/15 + m**2/5 + 388*m/5 - 12767. Determine u, given that k(u) = 0.
-194, -1, 1
Let g(j) be the second derivative of 2*j**6/15 + 144*j**5/5 + 2304*j**4 + 73728*j**3 - 1477*j. Factor g(l).
4*l*(l + 48)**3
Let x be 1*27065/(-45) - -8. Let t = -593 - x. Find o such that 0*o - t*o**2 - 2/9*o**3 + 2/3*o**4 + 0 = 0.
-2/3, 0, 1
Solve 170031464/9 + 467030/9*j**3 + 1670/9*j**4 + 171872960/9*j + 44356010/9*j**2 + 2/9*j**5 = 0 for j.
-277, -2
Let z(h) = -h**3 + 2*h**2 + 3*h + 2. Let b be z(3). Let r = 23079/4 - 5769. Factor -9/8*t + 0*t**b + 3/8*t**3 - r.
3*(t - 2)*(t + 1)**2/8
Let a(k) be the third derivative of k**6/240 - 17*k**5/60 - 71*k**4/48 - 3*k**3 + 255*k**2 + 3*k. What is p in a(p) = 0?
-1, 36
Factor -3*p**2 - 135/4 - 87/4*p.
-3*(p + 5)*(4*p + 9)/4
Determine z so that 92/9*z + 0 - 1/9*z**3 + 19/9*z**2 = 0.
-4, 0, 23
Let o be 960/2720 - 6/17. Solve o*i**2 + 4/7*i**3 + 6/7*i**4 + 0 + 0*i + 2/7*i**5 = 0 for i.
-2, -1, 0
Let z(p) be the second derivative of -5*p + 256/15*p**2 + 32/45*p**3 - 5 + 1/90*p**4. Factor z(y).
2*(y + 16)**2/15
Let x(n) = -6*n**2 - 11*n + 10. Let b be x(9). Let f = b + 578. Factor 0 + 5/2*t**f - 5/2*t**2 - 15*t.
5*t*(t - 3)*(t + 2)/2
Let s(v) = 4*v - 73. Let r be s(13). Let q be (-55)/(-15) - 7/r. Suppose 0*i + 1/3*i**5 - 2/3*i**q + 0 - 1/3*i**3 + 2/3*i**2 = 0. What is i?
-1, 0, 1, 2
Determine a, given that -236*a + 51*a**4 + 680*a**2 + 33134*a**3 - 32894*a**3 - 275*a**4 - 4*a**5 - 456 = 0.
-57, -1, 1, 2
Find d, given that -d**3 - 788271*d**2 + 788363*d**2 - 187*d + 2*d**3 + 94 = 0.
-94, 1
Let o(x) be the second derivative of 0 + 14/5*x**6 - 588/5*x**5 - 157*x - 1/42*x**7 + 0*x**2 + 0*x**3 + 5488/3*x**4. Let o(h) = 0. What is h?
0, 28
Let v(t) = -8*t**4 + 54*t**3 + 407*t**2 + 355*t. Let p(a) = a**4 - 3*a**3 - a**2 + a. Let l(c) = 5*p(c) + v(c). Factor l(b).
-3*b*(b - 20)*(b + 1)*(b + 6)
Suppose -2477*u = -2446*u. Let n(k) be the first derivative of 2/7*k**3 - 19 + 15/7*k**2 + u*k. Determine i so that n(i) = 0.
-5, 0
Factor -5*b**2 + 0 + 1/3*b**4 - 2*b**3 - 8/3*b.
b*(b - 8)*(b + 1)**2/3
Let n be 2/(-4) - (-153)/34. Suppose 2*o - 66 = -z, -42 - 96 = -n*o + z. Factor 20*g**5 - 50*g**4 + 25*g**5 - 10*g**3 + 6*g**2 - o*g**4 + 43*g**3.
3*g**2*(g - 1)**2*(15*g + 2)
Solve -2/3*c**3 + 12 - 2/3*c**4 - 26*c + 46/3*c**2 = 0 for c.
-6, 1, 3
Suppose 155 = -3*w - 31. Let v = -39 - w. Determine f, given that v*f**4 + f**5 + 8*f**5 + 36*f**3 + 12*f**2 + 10*f**4 = 0.
-2, -1, -2/3, 0
Let z be ((-4 - -4) + 1 + -1)/(-863 + 862). Let q(n) be the first derivative of 3*n**4 + 11 + 3*n**2 + 3/5*n**5 + 5*n**3 + z*n. Factor q(b).
3*b*(b + 1)**2*(b + 2)
Solve 1/2*m**4 + 0 + 61*m**3 + 1798*m**2 - 3844*m = 0 for m.
-62, 0, 2
Let t be (39/6)/(4433/4092). Let f(y) be the second derivative of 1/2*y**4 + y + 1/5*y**5 + 1/30*y**t + 2/3*y**3 - 6 + 1/2*y**2. Factor f(a).
(a + 1)**4
Let z(m) be the second derivative of 13*m + 32/7*m**2 - 1/42*m**4 - 4/21*m**3 - 1. Factor z(r).
-2*(r - 4)*(r + 8)/7
Let j(q) be the second derivative of 43*q**4/12 - 55*q**3/2 - 14*q**2 - 6042*q. Solve j(l) = 0.
-7/43, 4
Let v(s) be the second derivative of -s**4/12 - 17*s**3/2 - 25*s**2 - s + 566. Factor v(w).
-(w + 1)*(w + 50)
Let m = 531090 - 531042. Factor m*z + 9*z**2 + 64 + 1/2*z**3.
(z + 2)*(z + 8)**2/2
Let b = -268019/75 - -10721/3. Let q(j) be the first derivative of 36/5*j**2 + 0*j - 16/5*j**3 - 39 - 11/10*j**4 - b*j**5. Let q(f) = 0. What is f?
-6, 0, 1
Suppose -891/7*b**2 - 17496/7 - 1/7*b**4 + 51/7*b**3 + 6561/7*b = 0. Calculate b.
9, 24
Let j(c) be the first derivative of -c**6/39 - 2*c**5/13 + 3*c**4/2 + 274*c**3/39 + 142*c**2/13 + 96*c/13 - 845. Let j(m) = 0. What is m?
-8, -1, 6
Let x(w) be the third derivative of 2*w**3 - 29*w**2 - 1/20*w**5 + 1/2*w**4 - 1/40*w**6 + 0*w + 0. Factor x(h).
-3*(h - 2)*(h + 1)*(h + 2)
Suppose 0 = -2*i + 6, -w + 0*w - i = -389. Let u = w - 384. Factor -u*n - 12/7 - 2/7*n**2.
-2*(n + 1)*(n + 6)/7
Let 6919/4*l + 4977/2*l**2 + 1369/4 + 2315/2*l**3 + 3/4*l**5 + 229/4*l**4 = 0. What is l?
-37, -1, -1/3
Let c(d) = d**2 - 24*d + 49. Let q be c(22). Factor -20*a + 5*a**3 - 4*a**q + 4*a + 8*a**4 - 16*a**2 + 7*a**3.
-4*a*(a - 2)**2*(a + 1)**2
Let u be (-2)/(-2 + 17/((-95081)/(-11200))). Let o = u + 802. Factor -1/2*j**4 - 3/2*j**o + 1/2*j**5 + 1/2*j**2 + j + 0.
j*(j - 2)*(j - 1)*(j + 1)**2/2
Let m(h) be the third derivative of h**6/2520 - h**5/84 - 11*h**4/168 + h**3/6 - 86*h**2. Let s(y) be the first derivative of m(y). Factor s(z).
(z - 11)*(z + 1)/7
Suppose -10*v - 5740 = -45*v. Let x = -491/3 + v. Factor 1/3*c**2 - 2/3 + x*c.
(c - 1)*(c + 2)/3
Let z(s) be the second derivative of -1/10*s**3 + 18*s + 4*s**2 + 1/100*s**5 + 0 + 0*s**4. Let v(y) be the first derivative of z(y). Factor v(g).
3*(g - 1)*(g + 1)/5
Let g = -97 - -109. Suppose -13*w = -g*w - 36. Find b, given that 36*b**3 - b**4 + 4*b**4 + 4*b**4 + w*b + 9*b**4 - 104*b**2 + 16 = 0.
-4, -1/4, 1
Let n(a) be the second derivative of a**7/147 + 2*a**6/35 + 6*a**5/35 + 5*a**4/21 + a**3/7 + 1740*a. Factor n(m).
2*m*(m + 1)**3*(m + 3)/7
Solve -194*i**2 + 586/3*i + 190/3*i**3 - 196/3 + 2/3*i**4 = 0 for i.
-98, 1
Suppose 0 = 3*u + 56 + 25. Let r(k) = -21*k**4 + 27*k**2 + 27*k - 27. Let g(h) = -3*h**4 + 4*h**2 + 4*h - 4. Let i(z) = u*g(z) + 4*r(z). Factor i(t).
-3*t**4
Let s(c) = 18*c**2 - 1041*c - 9910. Let i(z) = 8*z**2 - 534*z - 4956. Let n(m) = 5*i(m) - 2*s(m). Let n(v) = 0. What is v?
-8, 155
Factor 0 + 320*o + 82*o**2 + 1/2*o**3.
o*(o + 4)*(o + 160)/2
Let f(m) be the second derivative of 845*m**2 + 3 - 26/3*m**3 + 1/30*m**4 - 15*m. Solve f(o) = 0.
65
Suppose -74 = 6*l - 104. Let p(n) = -n**2 + 7*n + 81. Let t be p(-6). Find c such that -9/4*c - 5/4*c**t + 1/2 + 13/4*c**2 + 1/2*c**l - 3/4*c**4 = 0.
-2, 1/2, 1
Let h(y) be the first derivative of y**3/2 + 705*y**2/2 + 1407*y/2 - 4569. Suppose h(w) = 0. Calculate w.
-469, -1
Let b be ((-54640)/(-90156))/(10/22). Factor -b*q**3 - 16/3*q**2 + 40/3 + 28/3*q.
-4*(q - 2)*(q + 1)*(q + 5)/3
Solve -48*q**3 - 46*q**3 - 2*q**2 + 123*q**3 + 6*q + 2 - 35*q**3 + 2 - 2*q**4 = 0.
-2, -1, 1
Suppose -47*s - 22129 = 4520. Let p be (162/s)/(4/(-49)). Solve -1 + p*f - 5/2*f**2 = 0 for f.
2/5, 1
Suppose -4*x + 1 = m - 18, 4*x - 3*m = 7. Factor -4*p**5 + 4760*p**2 + 33*p**x - 16*p**4 - 21060*p - 68*p**4 + 72*p**3 + 208*p**2 + 24300 - 33*p**4.
-4*(p - 3)**3*(p + 15)**2
Let u(o) be the first derivative of -3/4*o**4 - 83 - 13*o**3 - 33*o - 69/2*o**