Unit 8 Section 3 : Common Factors & Factorising

As well as being able to remove brackets by expanding expressions, it is also important to
be able to write expressions so that they include brackets; this is called factorisation.

Example Question 1
Factorise 4x + 6.

The first stage is to find break up 4x and 6 into factors, so that you can find everything that goes into both 4x and 6.
In this case 2 is the highest factor of both 4x and 6, so 2 will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.

We can check the answer by multiplying out the brackets: 2(2x+3) = 4x+6

Example Question 2
Factorise 18n + 24.

The first stage is to find break up 18n and 24 into factors, so that you can find everything that goes into both 18n and 24.
In this case 6 is the highest factor of both 18n and 24, so 6 will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.

We can check the answer by multiplying out the brackets: 6(3n+4) = 18n+24

Example Question 3
Factorise 4x + 6x.

In this case 2x is the highest factor of both 4x and 6x, so 2x will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.

We can check the answer by multiplying out the brackets: 2x(2x+3) = 4x+6x

Example Question 4
Factorise 3xy + 12xy.

In this case 3xy is the highest factor of both 3xy and 12xy, so 3xy will go outside the brackets.
The remaining factors of each term are left inside the brackets, where they are recombined.

We can check the answer by multiplying out the brackets: 3xy(y+4x) = 3xy + 12xy

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) Factorise 9x + 15

(b) Factorise 40x - 10

(c) Factorise 10x + 6x

(d) Factorise 15xy+25xy

(e) Factorise 4pq - 20pq + 8pq

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Important note on answering factorisation questions
It is important to make sure that you answer factorisation questions in
the correct way, or the computer may not mark your question correctly.

Please follow the following rules:
Example
Question
Right
Answer
Wrong
Answer
· do not put any spaces in your answer5x + 35 =
· always put the common factor first, then the brackets7x + 14y =
· keep the order of the terms the same as in the question6xy + 9x =
· do not use 1x or 1y instead of x or y4x + 12 =
· do not put more than one sign between terms4xy - 6x =
· make sure the expression is fully factorised10xy + 15x =
· letters within terms should be in alphabetical order10pq + 15pq =

Question 1
Factorise:
(a) 2x + 4 =
(b) 5x + 15 =
(c) 6x + 18 =
(d) 5x - 25 =
(e) 3x - 21 =
(f) 7x + 35 =
(g) 9x - 12 =
(h) 15x + 20 =
(i) 42x + 15 =
Question 2
Factorise:
(a)3x + 2x =
(b)5x + 10x =
(c)6x - 3x =
(d)6x - 4x =
(e)21x + 14x =
(f)15x - 25x =
Question 3
Factorise:
(a)xy + xz =
(b)xyz + 3yz =
(c)4pq - 8qr =
(d)5xyz + 20uxy =
(e)5xy - 4py =
(f)7xy + 12xz =
Question 4
Factorise:
(a)xy + xy =
(b)5xy - 35xy =
(c)22xy + 4xy =
(d)xyz + xyz =
Question 5
Factorise:
(a)3x + 9y + 18z =
(b)4x + 2x + 8xy =
(c)6x - 3xy + 12xz =
(d)5xz + 20x - 35xy =
(e)7x + 14xy - 21xyz =
(f)4x + 6xz + 15xy =


You have now completed Unit 8 Section 3
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Produced by A.J.Reynolds February 2004
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