AlgebraStudy Notes

Worked Example 3: Three Terms

Part of Factorising · GCSE GCSE Mathematics revision

This study notes covers Worked Example 3: Three Terms 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 6 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 6 of 13

Practice

12 questions

Recall

3 flashcards

Worked Example 3: Three Terms

Factorise: 12x³ + 8x² - 4x

Step 1 Find HCF of 12, 8, 4

HCF = 4

Step 2 Find common letter (lowest power)

x³, x², x → common is x

HCF = 4x

Step 3 Divide each term

12x³ ÷ 4x = 3x²

8x² ÷ 4x = 2x

-4x ÷ 4x = -1

Final Write answer

12x³ + 8x² - 4x = 4x(3x² + 2x - 1)

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 2: With Common Variable Common Mistakes 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

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Worked Example 2: With Common Variable

Common Mistakes