Basic Factoring Methods

In previous lessons, we’ve discussed how one goes about combining multiples of polynomials as well as multiplying two polynomials together. That is, we’ve taken products such as the following and “expanded” it by distribution of terms, to go from the left-hand side of the equation to the right-hand side of the equation; viz:

$$\begin{align} (x^2+1)(x^3+x)&=x^5+2x^3+x \end{align}$$

At times, it is more helpful to go from the right-hand side of an equation (like the above) to the left-hand side; that is, from its expanded form to an expression’s factored form.

In the following topics we develop several methods for factoring polynomials that will allow us to go from expanded expressions (like \(x^2+2x+1\) ) to their equivalent-but-factored form ( \((x+1)^2\), in our case). These factoring methods will effectively “undo” the process of distribution that we covered in previous lessons.