Factor $LaTeX: \displaystyle - 6 x^{3} - 9 x^{2} - 2 x - 3$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(6 x^{3} + 9 x^{2} + 2 x + 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(2 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(2 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 3$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(2 x + 3\right) +1 \cdot \left(2 x + 3\right)] = -\left(2 x + 3\right) \left(3 x^{2} + 1\right)$ .