AlgebraDeep Dive

Advanced: Factorising Quadratics

Part of Factorising · GCSE GCSE Mathematics revision

This deep dive covers Advanced: Factorising Quadratics 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 8 of 13 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 8 of 13

Practice

12 questions

Recall

3 flashcards

Advanced: Factorising Quadratics

When you expand (x + 3)(x + 2), you get x² + 5x + 6. Factorising is the reverse - given x² + 5x + 6, find the two brackets! The trick is finding two numbers that multiply to give the last number AND add to give the middle number.

Factorising quadratics - finding two numbers, sign rules, difference of squares

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.

Common Mistakes The "Two Numbers" Method 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 Rule

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

Factorising

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

12 questions on Factorising — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

Try PrepWise Free

Common Mistakes

The "Two Numbers" Method