How do I factor this:

Question

x^6-124x^3-125

Answer 1

well, I would let z = x^3

then
z^2 -124 z -125
(z-125)(z+1)
so

(x^3-125)(x^3 + 1)
we know 5^3 = 125
try dividing by (x^3-125) by x-5
sure enough
(x-5)(x^2+5x +25)(x^3 +1)
so try (x+1) on the (x^3+1) part
and get
(x-5)(x^2+5x+25)(x+1)(x^2-x+1)