Factor $LaTeX: \displaystyle - 50 x^{3} - 70 x^{2} - 10 x - 14$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(25 x^{3} + 35 x^{2} + 5 x + 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(5 x + 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(5 x + 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 7$ . This gives $LaTeX: \displaystyle -2[5 x^{2} \left(5 x + 7\right) +1 \cdot \left(5 x + 7\right)] = -2\left(5 x + 7\right) \left(5 x^{2} + 1\right)$ .