Factor $LaTeX: \displaystyle - 30 x^{3} - 15 x^{2} - 100 x - 50$ .

Factoring out the GCF $LaTeX: \displaystyle -5$ from each term gives $LaTeX: \displaystyle -5(6 x^{3} + 3 x^{2} + 20 x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(2 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 10$ , gives $LaTeX: \displaystyle 10(2 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 1$ . This gives $LaTeX: \displaystyle -5[3 x^{2} \left(2 x + 1\right) +10 \cdot \left(2 x + 1\right)] = -5\left(2 x + 1\right) \left(3 x^{2} + 10\right)$ .