Practice Factoring Polynomials by Grouping

Example 1

Factor the following polynomials completely.

(a) \(\begin{align*}2x^2-8\end{align*}\)

(b) \(\begin{align*}x^3+6x^2+9x\end{align*}\)

Solution:

(a) Look for the common monomial factor. \(\begin{align*}2x^2-8=2(x^2-4)\end{align*}\). Recognize  \(\begin{align*}x^2-4\end{align*}\) as a difference of squares. We factor \(\begin{align*}2(x^2-4)=2(x+2)(x-2)\end{align*}\). If we look at each factor we see that we can't factor anything else. The answer is \(\begin{align*}2(x+2)(x-2)\end{align*}\).

(b) Recognize this as a perfect square and factor as \(\begin{align*}x(x+3)^2\end{align*}\). If we look at each factor we see that we can't factor anything else. The answer is \(\begin{align*}x(x+3)^2\end{align*}\).