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 *x*^{2} + 7*x* + 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

2.

Factorise the following expression into a pair of linear brackets *x*^{2} - 9*x* + 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

3.

What is the correct answer when you factorise 3*x* - 9?

3(*x* - 3)

3(*x* + 3)

The common factor is placed outside the brackets

4.

What is the correct answer when you factorise 4*x*^{2}*y*^{3} + 8*x**y*^{2}?

4*x**y*^{2}(*x* + 2)

4*x**y*^{2}(*x**y* + 2)

4*x**y*^{2}(*x**y* + 4)

4*x**y*^{2}(*y* + 2)

Can you see why?

5.

What is the correct answer when you factorise *x*^{2} -5*x*?

The common factor is placed outside the brackets

6.

What is the common factor in the terms *x*^{2} -5*x*?

2

5

-5

7.

Factorise the following expression into a pair of linear brackets *x*^{2} + 8*x* + 12

(*x* - 2)(*x* - 6)

(*x* - 2)(*x* + 6)

(*x* + 2)(*x* - 6)

(*x* + 2)(*x* + 6)

Can you see the pattern?

8.

What are the highest common factors in 4*x*^{2}*y*^{3} + 8*x**y*^{2}?

2 and *x* and *y*^{2}

4 and *x*

4 and *x* and *y*^{2}

4 and *y*

4 is the highest common factor of 4 and 8, x is the highest common factor of x and x^{2} and y^{2} is the highest common factor of y^{2} and y^{3}

9.

Factorise the following expression into a pair of linear brackets *x*^{2} - 5*x* - 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

10.

What is the common factor in the terms 3*x* - 9?

3

6

9

3 is a part of both 3*x* and 9

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