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S3 BLOCK 8
Factorising
Learning Outcome
 I can factorise by considering the highest common factor.
1
Highest Common Factor
Factor
A factor is a whole number that divides exactly into a
given number.
Factors come in pairs.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
Highest Common Factor
The highest common factor (HCF) of two whole
numbers is the largest whole number which is a factor
of both.
HIGEST COMMON FACTOR
HCF
HCF
Examples
Find the highest common factor of each of the following pairs
(1) 8 and 12𝑥
(2) 6𝑥𝑦 2 and 4𝑥 2 𝑦
(3) 𝑎2 and 𝑎3
(1) Find the highest common factor of 8 and 12𝑥
Factors of 8 are: 1, 2, 4, 8
Factors of 12 are: 1, 2, 3, 4, 6, 12
The HCF of 8 and 12𝑥 is 4.
(2) Find the highest common factor of 6𝑥𝑦 2 and 4𝑥 2 𝑦
Factors of 6 are: 1, 2, 3
Factors of 4 are: 1, 2, 4
The HCF of 6𝑥𝑦 2 and 4𝑥 2 𝑦 is 𝟐𝒙𝒚.
(3) Find the highest common factor of 𝑎2 and 𝑎3
𝑎2 = 𝑎 × 𝑎
𝑎3 = 𝑎 × 𝑎 × 𝑎
The HCF of 𝑎2 and 𝑎3 is 𝒂𝟐 .
Factorise fully
I am practising factorising by considering the
highest common factor.
Success Criteria
• Write down the question.
• Work out the highest common factor.
• Write this down with brackets.
• Decide what has to go into the brackets.
Examples
Factorise fully
(1) 4𝑥 − 20
(2) 𝑥 2 + 5𝑥
(3) 𝑎𝑏 2 + 𝑎𝑏
(1) Factorise fully 4𝑥 − 20
The Highest Common Factor of 4𝑥 and 20 is 4.
4𝑥 − 20
= 4( 𝑥 − 5 )
(2) Factorise fully 𝑥 2 + 5𝑥
The Highest Common Factor of 𝑥 2 and 5𝑥 is 𝑥.
𝑥 2 + 5𝑥
= 𝑥( 𝑥 + 5 )
(3) Factorise fully 𝑎𝑏 2 + 𝑎𝑏
The Highest Common Factor of 𝑎𝑏 2 and 𝑎𝑏 is 𝑎𝑏.
𝑎𝑏 2 + 𝑎𝑏
= a𝑏( 𝑏 + 1 )
Challenge
Example
(i) Multiply out the brackets
(ii) Simplify
(iii) Factorise
(1)
Simplify 3 𝑥 − 2 + 5(𝑥 + 4)
Example
(i) Multiply out the brackets
(ii) Simplify
(iii) Factorise
(1)
3 𝑥 − 2 + 5(𝑥 + 4)
= 𝟑𝒙 − 6 + 𝟓𝒙 + 20
= 3𝑥 + 5𝑥 + 20 − 6
= 8𝑥 + 14
= 2(4𝑥 + 7)