AlgebraStudy Notes

Worked Example 2: With Common Variable

Part of Factorising · GCSE GCSE Mathematics revision

This study notes covers Worked Example 2: With Common Variable 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 5 of 13 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 13

Practice

12 questions

Recall

3 flashcards

Worked Example 2: With Common Variable

Factorise: 4x² + 10x

Step 1 Find HCF of numbers

HCF of 4 and 10 = 2

Step 2 Find common letters

x² has x×x, 10x has x

Common: x (lowest power)

Step 3 HCF = 2x

4x² ÷ 2x = 2x

10x ÷ 2x = 5

Final Write answer

4x² + 10x = 2x(2x + 5)

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.

Worked Example 1: Numbers Only Worked Example 3: Three Terms 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.

12 questions on Factorising — practise free

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

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Worked Example 1: Numbers Only

Worked Example 3: Three Terms