 Algebra Revision Foundation

09 -Factorise

What is Factorising?

A factor is a number that divides into another number.

The factors of 8 are 1, 2, 4 or 8. Factors work in pairs multiplying to give 8.

The common factors of 4 and 8 are 1, 2, 4.

8 is not a common factor.

Remember: Factorise means find the common factor.

Example:

i.e. Factorise the two terms: 3 + 6.

3 goes into 3 and 6 so it is the factor.

Put the common factor at the front of a bracket with two missing terms inside.

3 ( ☐ + ☐ )

A bracket means that when we multiply the factor outside the brackets with the terms inside we get the original terms.

So now we have to work out the missing terms that multiply by the factor 3 to give 3 and 6 (the originals)

3 + 6 →3(☐ + ☐) → 3(1 + 2)

because 3 × 1 = 3 and 3 × 2 = 6

It works the same for letters.

Factorise 3x + 6y

The common factor of 3x and 6y is 3 so factorising gives 3(x + 2y)

The common factor of 4x + x2 is x so factorising gives x(4 + x)

Q. Factorise the following:

1. 5x + 10y

2. 2x – 4xy

3. 2x2 + 4x