# Factoring Polynomials

When two or more algebraic expressions are multiplied, each expression is called a **factor** of the product. For instance, in the product , the factors are the , , and . Often we are given a product in its expanded form and we need to find the original factors. The process of finding these factors is called **factoring**.

In this tutorial, we confine our study of factoring to polynomials with integer coefficients. Thus, we shall not yet consider such possibilities as , because is not an integer.

Of course, we can factor any polynomial “trivially” by writing it as times itself or as times its negative. A polynomial with integer coefficients that cannot be factored (except trivially) into two or more polynomials with integer coefficients is said to be **prime**. When a polynomial is written as a product of prime factors, we say that it is **factored completely**.

__Removing a Common Factor__

The distributive property can be used to factor a polynomial in which all the terms contain a common factor. The following example illustrates how to “remove the common factor”.

__Example__:

Factor each polynomial by removing the common factor.

**(a) **

**(b) **

__Solution__:

**(a) **Here is a common factor of the two terms, since

and

Therefore,

**(b) **Here the common factor is , and we have