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Factorising quadratics
AQA GCSE Mathematics practice questions with step-by-step solutions
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EasyQuestion 1
[2 marks]Factorise:
x² + 9x + 20
Solution for Question 1
MediumQuestion 2
[2 marks]Factorise:
x² - 2x - 15
Solution for Question 2
HardQuestion 3
[3 marks]Factorise:
3x² + 11x + 6
Solution for Question 3
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Factorising quadratics is the reverse of expanding brackets. For x² + bx + c, find two numbers that multiply to c and add to b. For example, x² + 7x + 10 factorises to (x + 2)(x + 5) because 2 × 5 = 10 and 2 + 5 = 7.
When factorising ax² + bx + c where a ≠ 1, find two numbers that multiply to ac and add to b. Then use grouping or trial and improvement. For example, 2x² + 7x + 3: ac = 6, find 1 and 6. Rewrite as 2x² + 6x + x + 3, then factor as 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3).
Always check your answer by expanding. This catches sign errors and confirms your factorisation is correct.
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