AlgebraDeep Dive

The Two Numbers Method for Factorising

Part of Quadratic ExpressionsGCSE Mathematics

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 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 7

Practice

12 questions

Recall

22 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)

Keep building this topic

Read this section alongside the surrounding pages in Quadratic Expressions. That gives you the full topic sequence instead of a single isolated revision point.

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)

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