Syllabus Edition

First teaching 2023

First exams 2025

|

Factorising (CIE IGCSE Maths: Core)

Revision Note

Test yourself

Basic Factorising

What is factorisation?

  • A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)
    • 3(x  + 2) is factorised
      • It is 3 × (x  + 2)
    • 3x  + 6  is not factorised
    • 3xy  is factorised
      • It is 3 × x  × y
    • Numbers can also be factorised
      • 12 = 2 x 2 x 3
  • In algebra, factorisation is the reverse of expanding brackets
    • It's putting it into brackets, rather than removing brackets

  

How do I factorise two terms?

  • To factorise 12x2 + 18x  
    • Find the highest common factor of the number parts
      • 6
    • Find the highest common factor of the algebra parts
      • x
    • Multiply both to get the overall highest common factor
      • 6x
    • 12x2 + 18 is the same as 6 × 2x  + 6x  × 3
      • Using the highest common factor
    • Take out the highest common factor
      • Write it outside a set of brackets
      • Put the remaining terms, 2 + 3,  inside the brackets
    • This gives the answer
      • 6x (2x  + 3)
  • To factorise an expression containing multiple variables, e.g. 2a3b - 4a2b2
    • Use the same approach as above
    • Find the highest common factor of the number parts
      • 2
    • Find the highest common factor of the algebra parts
      • a and b appear in both terms
      • The highest common factor of a3 and a2 is a2
      • The highest common factor of b and b2 is b
      • a2b
    • Multiply both to get the overall highest common factor
      • 2a2b
    • 2a3b - 4a2b2  is the same as 2a2b  × a  -  2a2b  × 2b
      • Using the highest common factor
    • Take out the highest common factor
      • Write it outside a set of brackets
      • Put the remaining terms, a - 2b,  inside the brackets
    • This gives the answer
      • 2a2(a - 2b)

Examiner Tip

  • In the exam, check that your factorisation is correct by expanding the brackets!
  • Factorise mean factorise fully.
    • x (6+ 10) is not fully factorised but 2x (3x + 5) is.

Worked example

(a)

Factorise 5x + 15
 

Find the highest common factor of 5 and 15
 

5
 

There is no x in the second term, so no highest common factor in x  is needed
Think of each term as 5 × something

 

5 × x + 5 × 3
 

Take out the 5 and put + 3 in brackets
 

5( + 3)

5( + 3)

(b)
Factorise fully 30x2 - 24x
 
Find the highest common factor of 30 and 24
 
6
 
Find the highest common factor of x2  and x
 
x
 
Find the overall highest common factor by multiplying these together
  
6x

 

Think of each term as 6x  × something
 

6x  × 5x  - 6x  × 4
 

Take out the 6 and put 5x  - 4 in brackets
 

6x (5 - 4)

6x (5 - 4)

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.