Year 10 Interactive Maths - Second Edition

Factorisation using the Common Factor

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

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

Solution:

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

Study Another Topic in Chapter 10: Factorisation Techniques

[ Highest Common Factor ] [ Factorisation using the Common Factor ] [ The Difference of Two Squares ] [ Quadratic Trinomials ] [ Cross-Multiplication Method ] [ Factors of Quadratic Trinomials of the Type ax² + bx + c ] [ Use of Perfect Squares ] [ Use of Substitution ] [ Use of a Common Factor ] [ Factorisation of Four Terms ] [ Grouping 'Three and One' ] [ Real Numbers ] [ Completing the Square ] [ Problem Solving Unit ] [ Projects ] [ Symbols ] [ Index ]