Factor $LaTeX: \displaystyle - 2 x^{3} - 10 x^{2} + 6 x + 30$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(x^{3} + 5 x^{2} - 3 x - 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 5$ . This gives $LaTeX: \displaystyle -2[x^{2} \left(x + 5\right) -3 \cdot \left(x + 5\right)] = -2\left(x + 5\right) \left(x^{2} - 3\right)$ .