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# Level 7-8 Algebra - Factorisation

Factorisation is something you will come across in KS3 Maths when you are looking at algebra. 'Factorising' a number means breaking it down into smaller objects, or factors, which when multiplied together give the original. With numbers it's easy but with letters it's a little more complex.

Factorisation involves identifying a factor that is present in all of the terms. This gets put outside the bracket, and what is left over goes inside the bracket. The great thing is that you can always check your answer, by multiplying it out again.

You may also be asked to factorise quadratic expressions. These will have an x-squared term, usually an x-term, and a number. These factorise into double brackets. The trick here is to look for a pair of numbers that multiply to the number term, and add to the x-term.

That all sounds very complicated doesn't it? Well, the best way to become confident with factorisation is to keep doing it. This quiz will give you plenty of practice!

1.
Factorise the following expression into a pair of linear brackets x2 + 8x + 12
(x - 2)(x - 6)
(x - 2)(x + 6)
(x + 2)(x - 6)
(x + 2)(x + 6)
Can you see the pattern?
2.
What is the common factor in the terms x2 -5x?
2
5
-5
x
x is a part of both x2 and 5x
3.
What is the correct answer when you factorise 4x2y3 + 8xy2?
4xy2(x + 2)
4xy2(xy + 2)
4xy2(xy + 4)
4xy2(y + 2)
Can you see why?
4.
What are the highest common factors in 4x2y3 + 8xy2?
2 and x and y2
4 and x
4 and x and y2
4 and y
4 is the highest common factor of 4 and 8, x is the highest common factor of x and x2 and y2 is the highest common factor of y2 and y3
5.
What is the correct answer when you factorise x2 -5x?
x(x - 5)
x(x + 5)
x(x2 - 5)
x(x2 + 5)
The common factor is placed outside the brackets
6.
Factorise the following expression into a pair of linear brackets x2 - 5x - 6
(x - 1)(x - 6)
(x - 1)(x + 6)
(x + 1)(x - 6)
(x + 1)(x + 6)
The more often you factorise, the easier it will get
7.
Factorise the following expression into a pair of linear brackets x2 + 7x + 6
(x + 1)(x + 6)
(x - 1)(x + 6)
(x + 1)(x - 6)
(x - 1)(x - 6)
To check each of the answers it is necessary to multiply out the brackets. Remember that each term in each bracket is multiplied by each term in the other bracket
8.
What is the common factor in the terms 3x - 9?
x
3
6
9
3 is a part of both 3x and 9
9.
What is the correct answer when you factorise 3x - 9?
3(x - 3)
3(x + 3)
x(3 - 3)
x(3 + 3)
The common factor is placed outside the brackets
10.
Factorise the following expression into a pair of linear brackets x2 - 9x + 8
(x + 1)(x + 8)
(x +1)(x - 8)
(x -1)(x - 8)
(x -1)(x + 8)
After you have factorised several expressions you will begin to see patterns emerging that enable you to quickly arrive at the correct answer
Author:  Frank Evans