For p,q,r,s,a,b,c,d in Z-{0}, suppose px³ + qx² + rx + s = 0.

If px³ + qx² + rx + s can transform (ax - b)(cx - d)(ex - f),

we get

px³ + qx² + rx + s = (ax - b)(cx - d)(ex - f)

= acex³ + … -bdf

Compared with both sides, p = ace, s = -bdf.

Therefore,

s/p = -bdf / ace,

while the solutions of (ax - b)(cx - d)(ex - f) = 0 are

x = b/a, d/c, f/e.

Thus the candidates of solutions of the equation lies in s/p = -bdf / ace.