Question

How do you factor `6x^3 - 36x^2 - 162x`?

Answer 1

`6x^3-36x^2-162x = 6x(x^2-6x-27)`

`= 6x(x^2-(9-3)x-(9xx3)) = 6x(x-9)(x+3)`

Having separated the common `6x` factor out, it remained to try to find a factorization of `27` into two factors whose difference was `6`. There are not many choices to try and the pair `9, 6` works.