Question

How do you factor completely `12x^3-18x^2-8x+12`?

Answer 1

In problems like this, look for the first 2 terms and the second 2 terms to have a common factor - this one factored completely results in
`2(2x-3)(3x^2-2)`

Explanation:

In a problem like this one, we look for the (generally first two) terms and the second two terms and find ways to factor each of them to create a common factor to them both.

In this problem, we can see that the first two terms have a similar pattern to them as do the second two terms. And in fact, once we start factoring, there will be a common factor to them both.

Let's take the first 2 terms: `12x^3 - 18x^2`. We can factor out an `x^2` and also a 6, which leaves us with

`(6x^2)(2x-3)`

Can we factor something out of the second 2 terms, `-8x+12` to get us to `2x-3`? Yes we can - factor out a `-4` from each term. Which will give us

`(-4)(2x-3)`

So right now we have

`(6x^2)(2x-3)+(-4)(2x-3)`

We can take the common factor `2x-3` and factor that out and end up with

`(2x-3)(6x^2-4)`

Let's factor out a 2 from the `6x^2-4` term, which gives us the final answer of

`2(2x-3)(3x^2-2)`