Factorisation - general guide

Dr. J's Maths.com
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are explained in simple terms.

Basic factorisation approaches.
A general guide to deciding strategies for linear and quadratic expressions.

There are several methods which can be used independently or together to factorise linear and quadratic expressions. Remember:

linear expressions have a power of 1 for the variable - such as 2x + 6;
quadratic expressions have a power (or degree) of 2 for the variable - such as x² + 3x + 2 or x² - 4.

One technique we can use with such expressions is to factorise them - that is to rewrite these expressions in a form to show the product of their component factors.

For example, for the above expressions:

2x + 6 can be rewritten as 2(x + 3) where the 2 was a factor of both terms and the (x + 3) is the "left over" bit.
x² + 3x + 2 can be rewritten as (x + 1)(x + 2) and x² - 4 can be written as the product (x + 2)(x - 2).

We factorise expressions so that we can see their basic structures and that makes it easy to simplify expressions and to solve equations.

There are several basic approaches which can be used to factorise linear and quadratic expressions. These approaches are based on
the number of terms in an expression.

The following diagram summarises the overall strategy you should use:

The techniques to be used for each of these strategies are described separately by following the hyperlinks. Each technique has Test Yourself exercises with answers and solutions.

No. of terms	Technique to use.	Resource.
2	Common factor (2 & 3 terms)	Overview of technique.
		Common factor - Test Yourself 1.
		Common factor - Test Yourself 2.
	Difference between two squares	Overview of technique.
		2 Squares - Test Yourself 1.
		2 Squares - Test Yourself 1 Solutions.
		2 Squares - Test Yourself 2.
		2 Squares - Test Yourself 2 Solutions.
3	Cross method	Overview of technique.
	PSF	Overview of technique.


4		Overview of technique