66. Factor -t*b + 1/2*b**4 - 8*b**3 + 128 + 48*b**2.
(b - 4)**4/2
Let w be 1/4 + (-10)/(-24). Let t be ((-96)/4 + 23)/(((-1 - 2) + 1)/4). Factor w + 4*p**t - 14/3*p.
2*(p - 1)*(6*p - 1)/3
Suppose -15 = -3*b, 2*i + 2*b = 5*b + 1089. Factor 4*q**3 - 648*q + i*q + 36*q**2 - 8*q**3 + 64.
-4*(q - 4)**2*(q - 1)
Let q be 25 + (4/46 - (50/46 + -5)). Let x(p) be the first derivative of 4/3*p**3 - 10*p**2 - q + 24*p. Factor x(i).
4*(i - 3)*(i - 2)
Let y(l) = -3*l**4 - 3*l**3 + 54*l**2 + 168*l + 116. Let a(h) = -3*h + 1. Let b(j) = 4*a(j) + y(j). Solve b(o) = 0.
-2, 5
Let x = 780609 - 780605. Solve 50 - 45*y**x + 5/2*y**5 - 100*y**3 + 195/2*y - 5*y**2 = 0 for y.
-1, 1, 20
Determine c so that 54*c**2 - 15/4*c**3 - 384 - 144*c = 0.
-8/5, 8
Let o be 0/(10 - (23 - -4)). Let j(f) be the third derivative of -1/30*f**5 + 3*f**3 + 2/3*f**4 + f**2 + o - 2*f. Factor j(g).
-2*(g - 9)*(g + 1)
Let s be (-879)/(-586)*(-4 + (-160)/(-38)). Factor -s*j + 2/19 - 6/19*j**4 + 4/19*j**2 + 2/19*j**5 + 4/19*j**3.
2*(j - 1)**4*(j + 1)/19
Determine n so that 2/9*n**3 - 1600/9 + 394/9*n**2 - 1208/9*n = 0.
-200, -1, 4
Let c be (-14 + 9)/(3 - 4). What is o in 6*o - 3*o + 2*o + c*o**3 + o**2 + 9*o**2 = 0?
-1, 0
Find d such that 135/2 - 11*d - 1/2*d**2 = 0.
-27, 5
What is c in -9/4 - 21/4*c**5 + 9/2*c**2 + 21/2*c**3 - 9/4*c**4 - 21/4*c = 0?
-1, -3/7, 1
Let 0 + 45*p - 453/5*p**2 + 231/5*p**3 - 3/5*p**4 = 0. What is p?
0, 1, 75
Determine k, given that 62/11*k**2 - 192/11*k + 40/11*k**3 - 216/11 + 2/11*k**4 = 0.
-18, -3, -1, 2
Factor -2/11*t**3 - 392/11*t**2 + 0 - 390/11*t.
-2*t*(t + 1)*(t + 195)/11
Factor 3/2*q**2 - 1350 - 1/2*q**4 + 11*q**3 - 720*q.
-(q - 15)**2*(q + 2)*(q + 6)/2
Let w(a) = -a**2 + a - 1. Let x(j) = j**3 - 5*j**2 - 2*j + 5. Let b be x(1). Let l(c) = -8*c**2 + 148*c - 1300. Let n(r) = b*l(r) + 4*w(r). Factor n(v).
4*(v - 18)**2
Suppose -2*g - 3*g = 25. Let r be 6/g*(-145)/58. Factor 8*l**2 - 6*l**2 + 12*l**3 + r*l - 14*l**2.
3*l*(2*l - 1)**2
Let m = -12665/6 + 63349/30. Find l such that 1/5*l**5 + m*l**4 - 8/5 - 4*l - 14/5*l**2 + 1/5*l**3 = 0.
-2, -1, 2
Suppose -3098*c - 36 = -3110*c. Suppose -4 = 9*k - 40. Let 8/13*y + 2/13*y**k + 8/13 - 4/13*y**c - 6/13*y**2 = 0. Calculate y.
-1, 2
Let z be (-8512)/(-308) - (21 + 3). Let z*q**2 - 6/11 - 8/11*q = 0. Calculate q.
-3/10, 1/2
Let x(u) = u**3 - 5*u**2 - 25*u + 12. Let o = 87 + -79. Let t be x(o). Factor 10*j**2 - 30*j**3 - 46*j**5 + 25*j - 18 + 3 + 51*j**5 + 5*j**t.
5*(j - 1)**3*(j + 1)*(j + 3)
Let c be -5 - (-5 + -6) - (-2254)/56. Let v = c + -1283/28. What is s in -3/7*s**4 + 9/7*s**2 + 3/7*s**3 - v*s - 6/7 = 0?
-1, 1, 2
Let u(p) be the first derivative of -p**3/2 + 99*p**2/2 - 195*p/2 + 1090. Solve u(y) = 0 for y.
1, 65
Let t(o) be the first derivative of 4*o**3/9 - 142*o**2/3 - 728*o + 3414. Factor t(p).
4*(p - 78)*(p + 7)/3
Suppose -8261 + 305 = -26*l. Suppose 298*h = l*h. What is o in -2/11*o**5 + 8/11*o**3 + h*o**4 - 6/11*o - 4/11 + 4/11*o**2 = 0?
-1, 1, 2
Let q be -4 + (-37)/(-5) - (-2)/(-5). Let w be 6/(5*(-9)/(-465)). Factor 125*h - 4*h**2 - w*h**2 + 16*h**2 + 5*h**q.
5*h*(h - 5)**2
Let o = 3762/2807 - -150/401. Factor -6/7*p**3 + 9/7*p**2 - 12/7 + o*p - 3/7*p**4.
-3*(p - 1)**2*(p + 2)**2/7
Let -52*b + 18 - 40*b**2 + 42 - 79*b**3 + 53 - 17 + 75*b**3 = 0. Calculate b.
-8, -3, 1
Factor -14*r**2 + 110*r + 298*r - 341*r**2 + 43*r - 190 + 14*r + 5*r**4 + 75*r**3.
5*(r - 2)*(r - 1)**2*(r + 19)
Let -2/5*a**5 + 0*a**2 - 4*a**3 - 12/5 + 22/5*a + 12/5*a**4 = 0. What is a?
-1, 1, 2, 3
Solve -154*m**3 + 7/2*m**5 - 88*m + 0 - 45/2*m**4 - 234*m**2 = 0 for m.
-2, -4/7, 0, 11
Factor 0*p**2 + 0*p - 5/4*p**4 + 615/4*p**3 + 0.
-5*p**3*(p - 123)/4
Let i(w) be the second derivative of -25*w**7/441 - 92*w**6/63 - 1681*w**5/210 + 313*w**4/9 + 1940*w**3/63 + 200*w**2/21 + 2182*w. What is t in i(t) = 0?
-10, -1/5, 2
Let j(h) be the first derivative of -2*h**3/21 - 219*h**2/7 - 1628. Factor j(f).
-2*f*(f + 219)/7
Let p(d) be the second derivative of 3*d**6/2 - 6189*d**5/4 - 2590*d**4/3 + 13750*d**3/3 + 6880*d**2 - 2*d + 527. Find i such that p(i) = 0.
-2/3, 1, 688
Let u(d) be the third derivative of -d**7/105 - d**6/60 + 49*d**5/30 + 49*d**4/12 - 1710*d**2. Factor u(f).
-2*f*(f - 7)*(f + 1)*(f + 7)
Let s(q) = q**2 + 269*q - 1874. Let c(b) = -136*b + 936. Let i(h) = 9*c(h) + 4*s(h). Find j, given that i(j) = 0.
8, 29
Suppose -3*n + 0 = -6. Suppose 0*d + n*d = 4*x - 2394, 0 = -4*x - d + 2403. Let 605*c**2 + 14 + 6*c - x*c**2 + 6 - 31*c = 0. Calculate c.
1, 4
Let d(c) be the first derivative of -c**4/66 + 92*c**3/33 - 2116*c**2/11 - 294*c - 1. Let f(n) be the first derivative of d(n). Suppose f(l) = 0. Calculate l.
46
Let g be (-43 - -28)/((-210)/28). Suppose 5/2*k + 9/4 + 1/4*k**g = 0. Calculate k.
-9, -1
Suppose 0 = 4*u + 2*o - 8, 3*o = 2*u + 2*u - 8. Solve 20 + 2*r**3 - 30*r**2 + 16 + 62*r**u - 70*r = 0 for r.
-18, 1
Let j = 139921/30 + -4664. Let f(i) be the third derivative of -j*i**4 - 14*i**2 + 0*i**3 + 1/100*i**6 - 1/30*i**5 + 0 + 0*i. Factor f(y).
2*y*(y - 2)*(3*y + 1)/5
Suppose -31*j - 136 = -23*j. Let c = j - -22. Factor -32*m**2 + 20*m + 81*m**4 + 269*m**4 + 158*m**5 - 68*m**2 + 87*m**c - 15*m**3.
5*m*(m + 1)**2*(7*m - 2)**2
Let h(d) be the third derivative of -d**8/336 + 11*d**7/70 - 12*d**6/5 + 64*d**5/15 - 793*d**2 - 1. Let h(j) = 0. What is j?
0, 1, 16
Factor 44/17*r + 114/17 + 2/17*r**2.
2*(r + 3)*(r + 19)/17
Factor 0 - 2/3*t**3 - 412/3*t + 70*t**2.
-2*t*(t - 103)*(t - 2)/3
Factor 26*g**3 + 1/3*g**4 + 1444/3 + 988*g + 1597/3*g**2.
(g + 1)**2*(g + 38)**2/3
Let 30*g**3 + 115*g - 38922*g**2 + 38805*g**2 - 38 + 11*g**3 - g**4 = 0. Calculate g.
1, 38
Let h(d) = d**2 + 2*d - 18. Let b be h(-5). Let w be 17/3 + b/(-18)*-4. Factor 40*v**2 - 4 - 37*v**2 + w - v**3 - 3*v.
-(v - 1)**3
Let s = -457 - -2286/5. Suppose -15*j + 8*j = 0. Factor 1/5*l**4 + j*l + 3/5*l**2 - s*l**5 + l**3 + 0.
-l**2*(l - 3)*(l + 1)**2/5
Let x(h) be the third derivative of h**6/15 + 109*h**5/10 + 1107*h**4/2 - 1681*h**3/3 + 8932*h**2. Let x(l) = 0. What is l?
-41, 1/4
Let s = -2549 + 1476. Let u = -1071 - s. Suppose -9/8*n**u + 3 - 9/4*n + 3/8*n**3 = 0. What is n?
-2, 1, 4
Let y = 6404 + -6396. Let v(a) = a + 4. Let i be v(0). Solve -4*m + 18 - y*m**2 - 10 + i*m**2 = 0 for m.
-2, 1
Let m(w) = w**2 - 2*w - 3. Let t be m(3). Suppose -652*d + 1218 + 1045 = 959. Find n such that t*n + 1/2*n**d + 1/2*n**3 + 0 = 0.
-1, 0
Let a(x) = x**2 + 28*x + 190. Let n = -366 - -373. Let w(y) = y**2 + 28*y + 189. Let i(z) = n*a(z) - 6*w(z). Suppose i(c) = 0. Calculate c.
-14
Let b(j) be the first derivative of -111 + 1600*j + 80*j**2 + 4/3*j**3. Let b(i) = 0. What is i?
-20
Factor -16*h**2 + 1/3*h**4 + 1/3*h**3 + 128/3 + 80/3*h.
(h - 4)**2*(h + 1)*(h + 8)/3
Let 2/13*n**4 + 0 + 60/13*n**2 - 22/13*n**3 + 0*n = 0. What is n?
0, 5, 6
Let l(r) be the second derivative of r**6/375 + 121*r**5/250 - 41*r**4/25 - 142*r - 14. Suppose l(f) = 0. Calculate f.
-123, 0, 2
Let i(d) be the first derivative of -d**4/15 - 12*d**3/5 - 162*d**2/5 + 14*d + 166. Let q(c) be the first derivative of i(c). Factor q(s).
-4*(s + 9)**2/5
Let w(r) be the second derivative of -2*r**7/21 + 2*r**6/5 + 2*r**5 + 2*r**4/3 - 6*r**3 - 10*r**2 + 2*r - 370. Factor w(f).
-4*(f - 5)*(f - 1)*(f + 1)**3
Let s(g) = -27*g**3 + 186*g**2 - 135*g. Let z(m) = 11*m**3 - 75*m**2 + 54*m. Let w(p) = -5*s(p) - 12*z(p). Factor w(l).
3*l*(l - 9)*(l - 1)
Let l(p) = p**2 - 30*p - 297. Let k be l(-8). Factor 454586 + k*y**2 - 454586 - 8*y.
y*(7*y - 8)
Let x(v) = -3*v**3 - 93*v**2 - 273*v - 183. Let c(m) = -2*m**2 - m + 1. Let u(r) = 3*c(r) + x(r). Factor u(y).
-3*(y + 1)*(y + 2)*(y + 30)
Let k(z) = 7*z**2 + 247*z + 14884. Let l(m) = -19*m**2 - 740*m - 44652. Let p(x) = 8*k(x) + 3*l(x). Factor p(f).
-(f + 122)**2
Let k(x) be the third derivative of x**6/240 - 2*x**5/3 + 157*x**4/48 - 13*x**3/2 + 12*x**2 + 126*x. Find z, given that k(z) = 0.
1, 78
Solve -14*x**2 - 56198*x + 14*x**3 + 28 - 116*x**3 - 14*x**4 + 56300*x = 0 for x.
-7, -1, -2/7, 1
Let z(i) be the first derivative of -191 - 24*i + 7*i**2 - 1/3*i**3. Suppose z(x) = 0. What is x?
2, 12
Suppose -626 = 36*s + 526. Let q be (-1)/(8/s) + -2. Let 432/7 - 216/7*h - 2/7*h**3 + 36/7*h**q = 0. What is h?
6
Suppose -2292*d + 1873*d = -1164*d + 1490. Suppose -22/9*a + 8/3 - 2/9*a**d = 