Factor $LaTeX: \displaystyle - 12 x^{3} - 8 x^{2} - 21 x - 14$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(12 x^{3} + 8 x^{2} + 21 x + 14)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(3 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(3 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 2$ . This gives $LaTeX: \displaystyle -1[4 x^{2} \left(3 x + 2\right) +7 \cdot \left(3 x + 2\right)] = -\left(3 x + 2\right) \left(4 x^{2} + 7\right)$ .