Factor $LaTeX: \displaystyle 10 x^{3} - 50 x^{2} + 8 x - 40$ .

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