Factorising: GCSE Maths revision
Factorising is expanding in reverse: put an expression back into brackets. Examiners use it on Foundation (common factor) and Higher (quadratics and difference of two squares).
Common factor
Take out the highest common factor of every term.
Factorise 6x + 9
Check by expanding: 3 × 2x = 6x and 3 × 3 = 9.
Quadratic trinomials
For x² + bx + c, find two numbers that multiply to c and add to b.
Factorise x² + 7x + 12
Difference of two squares
Factorise x² − 25
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
Factorise 5x + 15
Factorise 4x² + 6x
Factorise x² + 5x + 6
Factorise x² − 9
Factorise x² − 8x + 15
Factorise 2x² + 7x + 3
Common mistakes
- Taking out a factor but leaving the 1 behind missing, e.g. writing 3(2x) instead of 3(2x + 3).
- Sign errors on negatives: x² − 5x + 6 is (x − 2)(x − 3), not (x + 2)(x − 3).
- Forgetting to check by expanding.
Answers and working
Frequently asked questions
How do I check factorising?
Expand your brackets. You should get back to the original expression.
What if the x² coefficient is not 1?
Find a pair of numbers that multiply to a×c and add to b, then factor by grouping. Or trial: (2x + ?)(x + ?).
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