来个直接的

8x^6+72x^5+bx^4+c^x3-687x^2-2160x-1700
= (2x+5)(2x+5)(2x+4)(x^3+ux^2+vx+w)
= (8x^3+56x^2+130x+100)(x^3+ux^2+vx+w)

==>

100w = -1700 ==> w = -17
100v + 130w = -2160 ==> v = 1/2
8u + 56 = 72 ==> u = 2

guess and verify
x^3+ux^2+vx+w = 0 has solution x = 2
..........