Factoring by Taking out the Common factors

A method of separating a common factor from the terms of an expression is called the factorization (or factorisation) by taking out the common factors.

Introduction

A mathematical expression can be formed by connecting two or many expressions with either plus or minus or combination of both. In some cases, a factor is commonly appeared in some terms or all terms of the polynomial. The common factor has to separate from the terms for writing the expression in simple form and this procedure is called the factorization by taking out the common factors.

Required knowledge

You must have knowledge on the following two concepts to understand how to factorise (or factorize) an expression by taking out the common factor.

Example

Let’s learn the concept of factoring a polynomial by taking out the common factors.

$5x^2+xy-6x$

For our convenience, write each term of this expression in factor form.

$=\,\,\,$ $5x \times x+x \times y-6 \times x$

Observe each term of this expression, there is a factor commonly appeared in each term. It can be taken out common from the terms by using the inverse operation of the distributive property of multiplication over addition or subtraction or combination of both.

$=\,\,\,$ $x \times (5x+y-6)$

$=\,\,\,$ $x(5x+y-6)$