Factor $LaTeX: \displaystyle - 2 x^{3} - x^{2} - 14 x - 7$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(2 x^{3} + x^{2} + 14 x + 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(2 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 1$ . This gives $LaTeX: \displaystyle -1[x^{2} \left(2 x + 1\right) +7 \cdot \left(2 x + 1\right)] = -\left(2 x + 1\right) \left(x^{2} + 7\right)$ .