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