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Syllabus Edition
First teaching 2021
Last exams 2024
Factorising (CIE IGCSE Maths: Core)
Revision Note
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 + 18x 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
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)
Write each term as 6x × "something"
6x × 5x - 6x × 4
"Take out" the 6x
6x(5x - 4)
6x(5x - 4)
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