Factor $LaTeX: \displaystyle 10 x^{3} + 16 x^{2} - 20 x - 32$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(5 x^{3} + 8 x^{2} - 10 x - 16)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(5 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(5 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 8$ . This gives $LaTeX: \displaystyle 2[x^{2} \left(5 x + 8\right) -2 \cdot \left(5 x + 8\right)] = 2\left(5 x + 8\right) \left(x^{2} - 2\right)$ .