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)
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.
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 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)