Factor $LaTeX: \displaystyle 50 x^{3} + 40 x^{2} - 20 x - 16$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(25 x^{3} + 20 x^{2} - 10 x - 8)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(5 x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(5 x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 4$ . This gives $LaTeX: \displaystyle 2[5 x^{2} \left(5 x + 4\right) -2 \cdot \left(5 x + 4\right)] = 2\left(5 x + 4\right) \left(5 x^{2} - 2\right)$ .