Question

factor the trinomial completely

12x^3-27x^2-27x

Answer 1

Hunt for common factors.

12x^3 = 2*2*3*x*x*x
27x^2 = 3*3*3*x*x
27x = 3*3*3*x

What's common?

Answer 2

2,3,x

Answer 3

2? No. That appears in only one term. There is no common 2.
There is a common 3.
There is a common x.

3x is the common factor that will help us.

The Distributive Property suggests:

12x^3-27x^2-27x = 3x(4x^2 - 9x - 9)