Factor $LaTeX: \displaystyle - 20 x^{3} - 32 x^{2} + 50 x + 80$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(10 x^{3} + 16 x^{2} - 25 x - 40)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(5 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(5 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 8$ . This gives $LaTeX: \displaystyle -2[2 x^{2} \left(5 x + 8\right) -5 \cdot \left(5 x + 8\right)] = -2\left(5 x + 8\right) \left(2 x^{2} - 5\right)$ .