Factorising quadratics practice questions

To factorise a quadratic like x squared plus 7x plus 12, find two numbers that multiply to the constant and add to the middle coefficient. Here 3 and 4 multiply to 12 and add to 7, so it factorises to (x plus 3)(x plus 4). Expanding the brackets checks the answer.

Factorising a quadratic means writing an expression like x² + 7x + 12 as a product of two brackets. It is the fastest route to solving quadratic equations, and it earns method marks even when the final answer goes wrong.

The method, step by step

1. Check the x² coefficient. If it is 1, the method below works directly.
2. Find the number pair. Look for two numbers that multiply to the constant and add to the x coefficient.
3. Write the brackets. Each number goes into its own bracket alongside x.
4. Expand to check. Multiply the brackets back out. You should recover the original expression.

Worked example

Common mistakes

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