General Strategy for Factoring Polynomials: example 7.59

$\begin{array}{ccccccc}\text{Is there a GCF?}\hfill & & & \text{Yes,}4x^4.\hfill & & & \hfill 4x^5+12x^4\hfill \\ & & & \text{Factor out the GCF.}\hfill & & & \hfill 4x^4\left(x+3\right)\hfill \\ \text{In the parentheses, is it a binomial, a}\hfill & & & & & & \\ \text{trinomial, or are there more than three terms?}\hfill & & & \text{Binomial.}\hfill & & & \\ \text{Is it a sum?}\hfill & & & & & & \text{Yes.}\hfill \\ \text{Of squares? Of cubes?}\hfill & & & & & & \text{No.}\hfill \\ \text{Check.}\hfill & & & & & & \\ \\ \text{Is the expression factored completely?}\hfill & & & & & & \text{Yes.}\hfill \\ \text{Multiply.}\hfill & & & & & & \\ \\ \\ 4x^4\left(x+3\right)\hfill & & & & & & \\ 4x^4·x+4x^4·3\hfill & & & & & & \\ 4x^5+12x^4✓\hfill & & & & & & \end{array}$