Generalized Factoring

Question

Factor the expression Completely:

4x³ −36x+ 72

Answer 1

4x³ - 36x + 72 has no rational roots, but 4x² - 36x + 72 = 4(x² - 9x + 18) = 4(x - 6)(x - 3).

Answer 2

4(x³-9x+18)

4(x(x²-9)+18)

4(x(x-3)(x+3)+18)

This is the best you can do, doesn't neatly factor beyond this.