Question

How do you factor `6x^3+34x^2-12x`?

Answer 1

`2x(3x-1)(1x+6)`

Explanation:

Given
`color(white)("XXX")6x^3+34x^2-12x`

First extract the obvious common factor of `(2x)` from each term:
`color(white)("XXX")(2x)(3x^2+17x-6)`

In the hopes of finding integer coefficient factors of `(3x^2+17x-6)`
we consider the integer factors of `3` and of `(-6)`
looking for a combination that will give us a sum of products `=17`

There are only a few possibilities. The diagram below might help understand the process:

The "working" combination is `(3x-1)(1x+6)`

Which gives us the complete factorization:
`color(white)("XXX")6x^3+34x^2-12x`
`color(white)("XXXXXXXXXXX")=(2x)(3x-1)(1x+6)`