Factor $LaTeX: \displaystyle - 42 x^{3} - 36 x^{2} - 63 x - 54$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(14 x^{3} + 12 x^{2} + 21 x + 18)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(7 x + 6)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(7 x + 6)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 6$ . This gives $LaTeX: \displaystyle -3[2 x^{2} \left(7 x + 6\right) +3 \cdot \left(7 x + 6\right)] = -3\left(7 x + 6\right) \left(2 x^{2} + 3\right)$ .