The Two Numbers Method for Factorising

Part of Quadratic Expressions · Section 4 of 8

Deep DiveUnit: AlgebraGCSE

This deep dive covers The Two Numbers Method for Factorising within Quadratic Expressions for GCSE Mathematics. Revise Quadratic Expressions in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 4 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

The Two Numbers Method for Factorising

To factorise x² + bx + c, find two numbers that:

  • Add to b (the coefficient of x)
  • Multiply to c (the constant term)

Example: Factorise x² + 7x + 12

Need two numbers that add to 7 and multiply to 12:

3 + 4 = 7 ✓ and 3 × 4 = 12 ✓

Therefore: x² + 7x + 12 = (x + 3)(x + 4)

Practice questions for Quadratic Expressions

Expand (x + 5)².

  • A. x² + 25
  • B. x² + 5x + 25
  • C. x² + 10x + 25
  • D. x² + 10x + 5
1 markfoundation

Explain how to recognise whether x² + 12x + 36 is a perfect square trinomial, and write it in factorised form.

2 markshigher

Quick recall flashcards

Expand (x + 6)(x - 4)
x² - 4x + 6x - 24 = x² + 2x - 24 (Be careful with negative signs!)
Expand (x + 2)(x + 5)
x² + 5x + 2x + 10 = x² + 7x + 10 (Using FOIL: First + Outer + Inner + Last)

12 questions on Quadratic Expressions — practise free

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