Factor $LaTeX: \displaystyle - 6 x^{3} - 42 x^{2} + 8 x + 56$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(3 x^{3} + 21 x^{2} - 4 x - 28)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(x + 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(x + 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 7$ . This gives $LaTeX: \displaystyle -2[3 x^{2} \left(x + 7\right) -4 \cdot \left(x + 7\right)] = -2\left(x + 7\right) \left(3 x^{2} - 4\right)$ .