Factorisation (factorization) using the Common Factor

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Year 10 Interactive Maths - Second Edition

Factorisation using the Common Factor

The factorisation (factorization) of 7x + 35 is 7(x + 5).

In general:

To factorise an algebraic expression, take out the highest common factor and place it in front of the brackets. Then the expression inside the brackets is obtained by dividing each term by the highest common factor.

Example 3

Factorise (Factorize) the following five expressions)

Solution:

Note:

The answer is neater if the first term in the bracket is positive. So, we use –3 as the common factor rather than 3.

Example 4

Factorise (Factorize) the following three expressions.

Solution:

Take out -1 as a common factor to factorise (Factorize) the expression.

Find and take out the HCF and then factorise (factorize).

Note:

An algebraic expression is said to be in its simplest form when it is written as a product of its factors.
The process of taking out a common factor is of great importance in algebra. With practice you will be able to find the highest common factor (HCF) readily and hence factorise the given expression.

Key Terms

taking out a common factor

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