Question

How do you factor `(x+3)^3-4x-12` ?

Answer 1

`(x+3)^3-4x-12 = (x+1)(x+5)(x+3)`

Explanation:

`(x+3)^3-4x-12 = (x+3)^3-4(x+3)`

`color(white)((x+3)^3-4x-12) = ((x+3)^2-4)(x+3)`

`color(white)((x+3)^3-4x-12) = (x^2+6x+9-4)(x+3)`

`color(white)((x+3)^3-4x-12) = (x^2+6x+5)(x+3)`

`color(white)((x+3)^3-4x-12) = (x+1)(x+5)(x+3)`