✗ 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)
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.
Practice questions for Factorising
Which is the correct factorisation of 6x + 15?
A student factorises x² + 5x + 4 as (x + 4)(x + 4). Explain why this is incorrect and give the correct factorisation.
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.