Question

How do you factor completely `4x^3-6x^2+2x-3`?

Answer 1

Use factoring to make the first 2 terms and the second 2 terms match, then factor them to arrive at
`(2x-3)(2x^2+1)`

Explanation:

Let's start with the original expression:

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

The thing to notice here is that the first 2 terms have coefficients of 4 and -6 and the second 2 terms have coefficients of 2 and -3. We can factor out `2x^2` from the first 2 terms to have it match to the second 2 terms, like this:

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

We can then factor the `2x-3` and end up with:

`(2x-3)(2x^2+1)`