Greatest Common Factor

The primary method for factoring polynomials will be factoring the greatest common factor.

While factoring in general it will also be the first thing that we must try as it will frequently simplify the problem.

In order to use this method all that we do is look at all the terms & determine if there is a factor which is in common to all the terms.  If there is, we will factor out polynomial.  Also note that in this matter we are actually only using the distributive law in reverse.  Keep in mind that the distributive law states that

                                                 a (b + c ) = ab + ac

In factoring out the greatest common factor we do this in reverse. We notice down that each of the term has an a in it and thus we "factor" it out utilizing the distributive law in reverse as follows,

ab + ac = a (b + c )