AlgebraStudy Notes

Common Mistakes

Part of Factorising · GCSE GCSE Mathematics revision

This study notes covers Common Mistakes 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 7 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 7 of 13

Practice

12 questions

Recall

3 flashcards

Common Mistakes

✗ 6x + 9 = 3(2x + 9) ✓ 6x + 9 = 3(2x + 3) - divide BOTH terms!

✗ 4x² + 8x = 4(x² + 2x) ✓ 4x² + 8x = 4x(x + 2) - x is also common!

✗ Forgetting to check by expanding ✓ ALWAYS expand to verify your answer!

Practice Questions

Q1 Factorise: 5x + 15 [1 mark]

[1] HCF = 5, so 5(x + 3)

Q2 Factorise: 3x² + 12x [2 marks]

[1] HCF = 3x

[1] 3x(x + 4)

Q3 Factorise: 6x² - 8x [2 marks]

[1] HCF = 2x

[1] 2x(3x - 4)

Q4 Factorise: 10y³ + 5y² - 15y [2 marks]

[1] HCF = 5y

[1] 5y(2y² + y - 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.

Worked Example 3: Three Terms Advanced: Factorising Quadratics 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

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Worked Example 3: Three Terms

Advanced: Factorising Quadratics