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

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(20 x^{3} + 25 x^{2} - 4 x - 5)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(4 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(4 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x + 5$ . This gives $LaTeX: \displaystyle 2[5 x^{2} \left(4 x + 5\right) -1 \cdot \left(4 x + 5\right)] = 2\left(4 x + 5\right) \left(5 x^{2} - 1\right)$ .