Factoring by Substitution

In this lesson, we learn how to factor a more complex polynomial using substitution. We previously learned how to factor a trinomial into the product of two binomials. We covered the easier scenario where a = 1, along with the more tedious scenario where a ≠ 1. We saw that we could factor the harder scenario using grouping or reverse FOIL. Here, we will learn to expand these concepts and factor a more complex polynomial by making a simple substitution. When we see a trinomial with a constant, a variable raised to a power, and the same variable raised to a power double that of the other, we can apply this substitution technique. First, we use our power to power rule to rewrite each power. We want the lower power to be a power raised to the first power. We want our higher power to be a power squared. Once this is done, we can make a simple substitution and factor. Lastly, we substitute back and we have factored a more complex polynomial using substitution.