Factor $LaTeX: \displaystyle 36 x^{3} + 72 x^{2} - 32 x - 64$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(9 x^{3} + 18 x^{2} - 8 x - 16)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -8$ , gives $LaTeX: \displaystyle -8(x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 2$ . This gives $LaTeX: \displaystyle 4[9 x^{2} \left(x + 2\right) -8 \cdot \left(x + 2\right)] = 4\left(x + 2\right) \left(9 x^{2} - 8\right)$ .