How to Factor Trinomials

In this section, we review how to factor a trinomial (a polynomial with three terms) into the product of two binomials (a polynomial with two terms), when the leading coefficient is one. When we factor trinomials, we essentially are reversing the FOIL process. Recall that FOIL stands for First Terms, Outer Terms, Inside Terms, and Last Terms. When the leading coefficient is one, it is very easy to find the first term of each binomial factor. For the final two terms, we look to find two integers whose sum is b (the coefficient for the variable to the first power) and whose product is c (the constant term). We will also take a look at two special case scenarios. First, we deal with factoring out the GCF, before beginning to factor. When we do this, it saves us from having additional factoring in the end. The second scenario involves factoring a trinomial with two variables involved. When this occurs, we treat the second variable as if it was a constant and factor using the same technique.