Syllabus Edition

First teaching 2021

Last exams 2024

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Factorising (CIE IGCSE Maths: Core)

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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, as it is 3 × (x + 2)
    • 3x + 6  is not factorised as it is "something" + "something"
    • 3xy is factorised as it is 3 × x × y
    • 12 can also be factorised: 12 = 2 x 2 x 3
  • In algebra, factorisation is the opposite of expanding brackets
    • it's "putting it into" brackets

  

How do I factorise two terms?

  • To factorise 12x2 + 18x  
    • The highest common factor of 12 and 18 is 6
    • The highest common factor of x2 and x is x
      • this is the largest letter that divides both x2 and x 
    • Multiply both to get the common factor
      • 6x
    • Rewrite each term in 12x2 + 18 as "common factor × something"
      • 6x × 2x + 6x × 3
    • "Take out" the common factor by writing it outside brackets
    • Put the remaining 2x + 3 inside the brackets
      • Answer: 6x(2x + 3)
      • Check this expands to give 12x2 + 18x

Examiner Tip

  • You can always check that your factorisation is correct by simply expanding the brackets in your answer!

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 needed
Write each term as 5 × "something"

 

5 × x + 5 × 3
 

"Take out" the 5
 

5(x + 3)

5(x + 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 common factor (by multiplying these together)
  
6x

 

Write each term as 6x × "something"
 

6x × 5x - 6x × 4
 

"Take out" the 6x
 

6x(5x - 4)

6x(5x - 4)

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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.