Factor $LaTeX: \displaystyle 50 x^{3} - 10 x^{2} - 80 x + 16$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(25 x^{3} - 5 x^{2} - 40 x + 8)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(5 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -8$ , gives $LaTeX: \displaystyle -8(5 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x - 1$ . This gives $LaTeX: \displaystyle 2[5 x^{2} \left(5 x - 1\right) -8 \cdot \left(5 x - 1\right)] = 2\left(5 x - 1\right) \left(5 x^{2} - 8\right)$ .