4. Suppose o*j - 59 = -8. Factor 10*y**2 - 6 - 8*y**3 + 5 + 14*y - j.
-2*(y - 2)*(y + 1)*(4*y - 1)
Factor 141/2*i**3 + 3/2*i**4 + 0 - 468*i - 399*i**2.
3*i*(i - 6)*(i + 1)*(i + 52)/2
Let a(l) be the third derivative of -l**7/21 + 11*l**6/80 + 7*l**5/80 - 5*l**4/6 + 11*l**3/8 + 3*l**2 + 2*l - 504. Let a(d) = 0. Calculate d.
-11/10, 3/4, 1
Let y = 28676507/24574 + 529/2234. Let o = -1167 + y. Factor -32/11 - o*q**2 - 16/11*q.
-2*(q + 4)**2/11
Suppose -3*l + j = -221, l = -l - 2*j + 150. Suppose m + r = 16, 4*m - r + 3*r - l = 0. Factor 38*a + 2*a**3 - 8*a**2 - m*a - 19*a + 8.
2*(a - 4)*(a - 1)*(a + 1)
Suppose 3*w - 5*j = w + 127, -4*w + 214 = -2*j. Determine a, given that -17*a**3 + w*a + 9*a**3 + 20*a**2 - 55*a - 8 = 0.
-1/2, 1, 2
Suppose 455 = -24*f - 11*f. Let a(z) = 3*z**2 + 45*z + 168. Let n(d) = -7*d**2 - 89*d - 334. Let m(r) = f*a(r) - 6*n(r). What is p in m(p) = 0?
-3, 20
Factor -1682/17*h**3 + 0 + 0*h - 116/17*h**4 - 2/17*h**5 + 0*h**2.
-2*h**3*(h + 29)**2/17
Let k(m) be the third derivative of m**6/96 + 5*m**5/24 - 715*m**4/96 - 605*m**3/2 - 16*m**2 - 6. What is x in k(x) = 0?
-11, 12
Let l be 360/25 + (-88)/11 + -4. Factor 0 - l*u**2 + 0*u**3 + 9/5*u**4 + 3/5*u**5 + 0*u.
3*u**2*(u - 1)*(u + 2)**2/5
Let b(h) = -h**3 + 1070*h**2 - 11635*h + 10503. Let o(g) = -268*g**2 + 2908*g - 2626. Let u(j) = -2*b(j) - 9*o(j). Find q, given that u(q) = 0.
-146, 1, 9
Factor 105118*c - 2*c**3 + 10 - c**2 + 7*c**2 - 105100*c.
-2*(c - 5)*(c + 1)**2
Let b = -68935 - -68935. Factor 6/7*c**4 + 0*c + 0*c**2 + 0*c**3 + 2/7*c**5 + b.
2*c**4*(c + 3)/7
Let m(a) be the third derivative of a**7/630 - 31*a**6/360 + 169*a**5/90 - 365*a**4/18 + 100*a**3 + 9404*a**2. Let m(u) = 0. What is u?
2, 9, 10
Let m be (-3)/(2*3/(-18)). Let v be 0/5 - -4 - 0/13. Factor 4*c**4 + c + 2*c**v + 6*c**2 + m*c - 8 - 4*c**4 - 10*c**3.
2*(c - 4)*(c - 1)**2*(c + 1)
Let n = 6081 + -12157/2. Let q(z) be the first derivative of -5 - n*z**2 + 5/3*z**3 + 0*z. Suppose q(y) = 0. What is y?
0, 1
Let m(v) = -v**2 - 3*v - 2. Let y(r) = 4*r**3 - 155*r**2 + 443*r - 286. Let o(a) = -m(a) - y(a). Factor o(g).
-4*(g - 36)*(g - 2)*(g - 1)
Let i(n) = -n**3 + 5*n**2 + 2*n - 1. Let j(k) = 18*k**3 - 648*k**2 + 27615*k - 27060. Let c(f) = 15*i(f) + j(f). Factor c(s).
3*(s - 95)**2*(s - 1)
Let u(b) be the first derivative of -b**4/6 - 562*b**3/9 + 1136*b**2/3 - 760*b + 696. Determine h, given that u(h) = 0.
-285, 2
Let x(v) be the second derivative of v**5/20 + v**4/3 + v**3/6 - v**2/2 + 91*v. Let f be x(-3). Factor 0 + 2/5*h**f + 0*h + 2/5*h**2 - 2/5*h**4 - 2/5*h**3.
2*h**2*(h - 1)**2*(h + 1)/5
Suppose 3*a - 2 = 2*s, 1598*a - 1605*a - 4*s = 4. Determine p, given that -1/2*p**3 - 1/4*p**2 + a + 7/4*p**4 - p**5 + 0*p = 0.
-1/4, 0, 1
Let n(w) be the third derivative of 0*w - 31/10*w**5 - 11 - w**2 - 59/3*w**4 - 20*w**3 - 7/60*w**6. Suppose n(a) = 0. What is a?
-10, -3, -2/7
Let t = -51265/29667 + 2/2697. Let p = -1/77 - t. Factor p*b**3 - 3/7 + 3*b**2 + 6/7*b.
3*(b + 1)**2*(4*b - 1)/7
Factor 348/5*a + 8*a**3 + 1172/5*a**2 + 0.
4*a*(a + 29)*(10*a + 3)/5
Let b(k) be the second derivative of -k**4/48 - 17*k**3/8 + 59*k**2 + 5989*k. Solve b(y) = 0 for y.
-59, 8
Let o(x) be the third derivative of x**8/84 - 26*x**7/105 - x**6/2 + 171*x**5/5 - 81*x**4 - 103*x**2. Factor o(z).
4*z*(z - 9)**2*(z - 1)*(z + 6)
Let x be ((-5)/10)/((-2)/(-36)). Let d be (-16)/x - 1/(-18)*4. Find i, given that 0 - 4/3*i - 2/3*i**d = 0.
-2, 0
Let z be 0 + (-14)/(-7) + 330/60. Suppose 5 - 31/2*v**2 + 47/2*v - z*v**4 - 83/2*v**3 = 0. What is v?
-5, -1, -1/5, 2/3
Let h(r) = 27*r**3 + 222*r**2 - 213*r - 438. Let w(d) = -157*d**3 - 1333*d**2 + 1279*d + 2630. Let x(o) = -35*h(o) - 6*w(o). Factor x(z).
-3*(z - 75)*(z - 2)*(z + 1)
Let j = -73 + 31. Let m be (-1)/3 - 182/j. Solve 26 + 26 + m*i**4 - 11*i**3 - 52 - 3*i**2 = 0.
-1/4, 0, 3
Factor -4/5*m**3 - 1/5*m**4 + 4/5*m + 1/5*m**2 + 0.
-m*(m - 1)*(m + 1)*(m + 4)/5
Suppose -19*v - 13*v + 1632 = 0. Suppose 4*c = v*c - 94. Determine z so that -1/8 + 1/4*z + 3/8*z**c = 0.
-1, 1/3
Let l(f) be the third derivative of f**6/600 + 161*f**5/300 + 164*f**4/3 + 640*f**3/3 - 1478*f**2. Factor l(v).
(v + 1)*(v + 80)**2/5
Solve 0 - 1/2*d**2 - 87/2*d = 0 for d.
-87, 0
Let o be 12/5 + (-2)/5. Let a = 489075 - 489075. Factor 6/7*c**o + 8/7*c**3 + 0 + a*c + 2/7*c**4.
2*c**2*(c + 1)*(c + 3)/7
Let s = -408 + 413. Suppose 0*w - 5*z = -5*w + 20, 10 = -s*z. Suppose -1/3*r**w + 1/3*r + 1/3*r**4 + 0 - 1/3*r**3 = 0. Calculate r.
-1, 0, 1
Let y(s) be the second derivative of s**4/72 - 8*s**3/9 + 16*s**2 - 148*s. Determine h, given that y(h) = 0.
8, 24
Let t(o) = 6*o**2 + 242*o - 5260. Let a be t(-56). Factor 1058/19*z + 2/19*z**a + 1150/19*z**2 + 94/19*z**3 + 0.
2*z*(z + 1)*(z + 23)**2/19
Let v = 1628 - 1623. Let y(o) be the third derivative of 0*o - 8/105*o**7 - 2/3*o**4 + 1/84*o**8 + 0*o**3 + 15*o**2 + 0 + 1/10*o**6 + 4/15*o**v. Factor y(z).
4*z*(z - 2)**2*(z - 1)*(z + 1)
Factor 11 + 1/5*a**2 + 16/5*a.
(a + 5)*(a + 11)/5
Factor 7203/5*y**4 - 28518/5*y**3 + 12/5 + 1164/5*y + 27639/5*y**2.
3*(y - 2)**2*(49*y + 1)**2/5
Factor 31/2*h**2 + 19/4*h**3 + 5/2 + 53/4*h.
(h + 1)*(h + 2)*(19*h + 5)/4
Let x = -61261/35 - -8763/5. Let r(b) be the first derivative of -4 - 4/7*b**2 + 20/21*b**3 - x*b - 3/14*b**4. Factor r(y).
-2*(y - 2)**2*(3*y + 2)/7
Let r(j) = j**2 - j + 9. Let k be r(10). Suppose -2*p + k = 93. Factor 0 + 1/2*t**p + 1/2*t**4 + 0*t - t**2.
t**2*(t - 1)*(t + 2)/2
Let h(q) be the second derivative of 9*q**6/10 - 261*q**5/20 + 181*q**4/4 - 93*q**3/2 + 21*q**2 - 92*q - 5. Factor h(c).
3*(c - 7)*(c - 2)*(3*c - 1)**2
Let q(l) be the third derivative of l**6/40 + 23*l**5/60 - 35*l**4/24 + 3*l**3/2 + 2*l**2 - 968. Factor q(k).
(k - 1)*(k + 9)*(3*k - 1)
Let m = 221798693356/8371 + -26496080. Let j = -6/761 + m. Factor 0 + 2/11*z**4 + 8/11*z**3 + j*z**2 + 4/11*z.
2*z*(z + 1)**2*(z + 2)/11
Let a(t) be the second derivative of -t**4/30 + 4*t**3 - 116*t**2/5 + 53*t + 9. Find v, given that a(v) = 0.
2, 58
Let g = 3 + 122. Let t = -3698 + 4366. Factor t*l**2 - 1678*l**3 + 320*l**4 - 154*l - g*l**5 + 12 + 381*l**5 + 574*l**3 + 2*l.
4*(l - 1)*(l + 3)*(4*l - 1)**3
Suppose 515*o = 519*o - 3*u - 45, -4*u - 60 = 4*o. Factor 2/11*m**2 - 2/11*m + o - 2/11*m**4 + 2/11*m**3.
-2*m*(m - 1)**2*(m + 1)/11
Suppose 323*d + 862*d - 2350 + 64*d**2 - 55*d**2 - 14*d**2 = 0. What is d?
2, 235
Let r = 2443 + -2149. Let c be (20/15 - 6)*(-36)/r. Factor -2/7*x**2 - 2/7 + c*x.
-2*(x - 1)**2/7
Let c = -11802 - -11806. Let t(u) be the second derivative of 0 - 1/96*u**c + 0*u**2 + 5/48*u**3 + 32*u. Factor t(f).
-f*(f - 5)/8
Suppose 54*o + 4 = 5*o + 51*o. Let u(k) be the first derivative of 5/6*k**o + 5/9*k**3 - 10/3*k + 12. Solve u(d) = 0 for d.
-2, 1
Let m(v) be the second derivative of -v**7/56 - v**6/5 - 39*v**5/80 + 11*v**4/8 + 4*v**3 - 12*v**2 - 2351*v. Solve m(j) = 0 for j.
-4, -2, 1
Let u(i) be the first derivative of i**5/5 - 37*i**4/2 - 76*i**3 - 115*i**2 - 77*i + 7151. Factor u(b).
(b - 77)*(b + 1)**3
Suppose 2*g + 4 = 6, 2*s - 2*g + 136 = 0. Let f = s + 70. Let 6*c**4 - 3*c**5 + 6*c**2 - 2*c - c - f - 9*c**4 + 6*c**3 = 0. Calculate c.
-1, 1
Suppose 8*q - 159 + 103 = 0. Let x(g) = 8*g - 52. Let s be x(q). Factor 2/17*z**5 + 0 + 0*z**2 - 4/17*z**s + 0*z + 2/17*z**3.
2*z**3*(z - 1)**2/17
Let h be -10 + (315/(-108))/(20/(-72)). Determine l so that h*l**4 + 0*l**2 - 8 + 2*l**3 - 8*l = 0.
-2, 2
Let u(v) = 792*v**4 + 4564*v**3 + 3396*v**2 + 896*v + 72. Let m(n) = n**4 - 1. Let x(w) = 8*m(w) - u(w). Determine o so that x(o) = 0.
-5, -2/7, -1/4
Let j = -12983332/15 - -865556. Factor 2/15*z**2 - 64/15 + j*z.
2*(z - 4)*(z + 8)/15
Let v = -2/34011 + 34015/68022. Factor 3/2*i + 0 + v*i**3 - 2*i**2.
i*(i - 3)*(i - 1)/2
Let g(n) = 3*n**3 + 102*n**2 + 283*n. Let k(c) = -19*c**3 - 612*c**2 - 1691*c. Let m(s) = 39*g(s) + 6*k(s). Suppose m(t) = 0. What is t?
-99, -3, 0
Let h(y) = 2*y**3 - 3*y**2 - y + 2. Let d(i) = 21*i**3 - 45*i**2 - 297*i + 1938. Let k(q) = -d(q) + 9*h(q). What is x in k(x) = 0?
-10, 8
Factor -3*d**4 - 197 + 392*d - 8*d**3 + 855*d**2 + 5*d**4 - 1043*d**2 - 1.
2*(d - 11)*(d - 1)**2*(d + 9)
Let d(t) = 4*t + 31. Let h(l) = -3*l**2 - 2*l + 1. Let f be h(-2). Let k be d(f). Factor k*z**3 + 25*z**2 + 30*z + z**3 - 9*z**3.
-5*z*(z - 6)*(z + 1)
Let n = -43