Factor $LaTeX: \displaystyle - 12 x^{3} - 36 x^{2} + 14 x + 42$ .

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