How it works

A quadratic expression x² + bx + c can be factorised into two brackets (x + p)(x + q) where p and q multiply to give c and add to give b. When the coefficient of x² is not 1, factors of both the first and last terms must be considered. Factorising is the reverse of expanding brackets and is used to solve quadratic equations.

The method

1. 1.Find two numbers that multiply to give c and add to give b
2. 2.Write the expression as two brackets using these numbers
3. 3.Expand to check the brackets give back the original expression

Worked example

Factorise x² + 7x + 12.

1. Find two numbers that multiply to 12 and add to 7: 3 and 4
2. (x + 3)(x + 4)

Worked example

Factorise x² - 2x - 15.

1. Find two numbers multiplying to -15 and adding to -2: -5 and 3
2. (x - 5)(x + 3)

Common mistakes

• Choosing two numbers that add correctly but multiply incorrectly (or vice versa)
• Forgetting to consider negative factor pairs
• Not checking the factorisation by expanding it back out