Year 9: Factorisation

Factorisation is the process of breaking down an expression into a product of its factors.

What is a Factor?

A factor of a number is a number that divides evenly into that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Common Factorisation Techniques

Difference of Squares

a² - b² = (a + b)(a - b)

Example: x² - 9 = (x + 3)(x - 3)

Simple Trinomials (x² + bx + c)

Find two numbers that multiply to 'c' and add up to 'b'.

Example: x² + 5x + 6 = (x + 2)(x + 3)

Simple Trinomials (x² + bx + c) - Negative Version

For example: x² - 5x + 6 = (x - 2)(x - 3)

Steps for Factorising

1. Identify the type of expression.
2. Apply the appropriate technique.
3. Check your answer by expanding the factored expression.