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

1 Answer
Alan P.
Oct 9, 2015

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:
enter image source here
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)

Related questions
See all questions in Factoring Completely
Impact of this question
1599 views around the world
You can reuse this answer
Creative Commons License