AlgebraKey Facts

The "Two Numbers" Method

Part of Factorising — GCSE Mathematics

This key facts covers The "Two Numbers" Method within Factorising for GCSE Mathematics. Revise Factorising in Algebra for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 9 of 12 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 9 of 12

Practice

12 questions

Recall

3 flashcards

The "Two Numbers" Method

For x² + bx + c, find two numbers that:

MULTIPLY to give c

ADD to give b

Example: x² + 5x + 6

Need: multiply to 6, add to 5
Numbers: 2 and 3 (2×3=6, 2+3=5)
Answer: (x + 2)(x + 3)

Keep building this topic

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

Advanced: Factorising Quadratics Worked Example: Quadratic - Both Positive Factorising = Reverse of Expanding The Key Idea

Practice Questions for Factorising

Which is the correct factorisation of 6x + 15?

A. 3(2x + 5)
B. 6(x + 9)
C. 3(2x + 15)
D. 2(3x + 7)

1 markfoundation

A student factorises x² + 5x + 4 as (x + 4)(x + 4). Explain why this is incorrect and give the correct factorisation.

2 marksstandard

Quick Recall Flashcards

Factorising

Take out highest common factor: 6x + 9 = 3(2x + 3)

Factorising Rule

Find the HCF of all terms (numbers AND letters), put outside bracket, divide each term for inside.

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Advanced: Factorising Quadratics

Worked Example: Quadratic - Both Positive