Introduction to factorising

Introduction to Factorising

What is Factorising?

Factorising is the process where you express a mathematical expression as a product of its factors.
A factor is a number or algebraic term that divides another number or algebraic term exactly.

Basic Principles

A simple example of factorising could be taking the number ‘12’ and expressing it as ‘3 x 4’ or ‘2 x 6’. In each case, the numbers ‘3’ and ‘4’, ‘2’ and ‘6’ are considered the factors.
This extends to algebraic expressions too. For instance, ‘3x’ can be factorised to ‘3 x x’.
Factorising is used to simplify complex expressions, break them into manageable parts and to solve algebraic equations.

Process of Factorising

First, identify if there are any common factors in the terms of the expression.
If there are, simply divide all the terms by that common factor.
Write your expression as a product of the common factor and the remaining once factorised expression.

Examples

An expression like ‘2x + 4’ can be written as ‘2(x + 2)’, where ‘2’ is the common factor and ‘(x + 2)’ is the remaining expression.
An expression like ‘3y^3 - 9y^2 + 6y’ can be expressed as ‘3y(y^2 - 3y + 2)’, factorising by taking out the common factor of ‘3y’.

Extra Notes

Learning to factorise helps greatly with solving quadratic equations, simplifying expressions, and understanding higher level algebraic concepts.
It’s important to always look for the largest common factor when factorising.
Sometimes, expressions can be factorised multiple times until they are fully simplified. Ensure you’ve fully factorised for the most simplified form.