Factoring by Grouping

In this section, we review how to factor a four-term polynomial using factoring by grouping. With this method, our goal is to produce and factor out a common binomial factor. We begin the process by factoring out the GCF from the four-term polynomial. If the GCF is 1, we proceed to our next step. We then want to arrange our terms into two groups of two, such that each group has a common factor. In some cases, we may have to use a common factor of 1 or -1. We then factor out the GCF or –(GCF) from each group. We look to see if the result yields a common binomial factor. When this occurs, we factor out the common binomial factor and report our answer. In some cases, we fail to get a common binomial factor on the first try. When this occurs, we may be able to rearrange terms and try a different grouping.