How to Factor by Grouping

Description

A detailed tutorial on how to factor by grouping. Step by step tutorial including several examples of how to factor by grouping for reference.

Overview

There are many different ways to factor, but one of the easiest ways is to factor by grouping. If you factor by grouping, it means that you are given (or split terms up into) 4 terms, and then split those 4 terms into two groups each consisting of 2 terms. Put parenthesis around these groups. Here’s an example:

axt + ax – at – a = (axt + ax) – (at – a)

Now you want to pull something out of the parenthesis. Whatever is left in your parenthesis should be exactly the same for both sets of parenthesis – it doesn’t matter if what was pulled out is different. Then, you create another set of two parenthesis and multiply them together – form two binomials that you could solve by FOIL, basically. In the first set goes what you pulled out of the parenthesis, for instance if you pulled a 4x out of one and a -5 out of the other, your first set would be (4x – 5). The second set of parenthesis is whatever was left in your parenthesis on your first set. Now you can solve the problem how you would normally would solve a factoring problem.

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