Factor $LaTeX: \displaystyle 18 x^{3} + 72 x^{2} - 10 x - 40$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(9 x^{3} + 36 x^{2} - 5 x - 20)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 4$ . This gives $LaTeX: \displaystyle 2[9 x^{2} \left(x + 4\right) -5 \cdot \left(x + 4\right)] = 2\left(x + 4\right) \left(9 x^{2} - 5\right)$ .