Factor $LaTeX: \displaystyle - 10 x^{3} - 25 x^{2} - 2 x - 5$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(10 x^{3} + 25 x^{2} + 2 x + 5)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(2 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(2 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 5$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(2 x + 5\right) +1 \cdot \left(2 x + 5\right)] = -\left(2 x + 5\right) \left(5 x^{2} + 1\right)$ .