Factor $LaTeX: \displaystyle - 32 x^{3} - 48 x^{2} + 28 x + 42$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(16 x^{3} + 24 x^{2} - 14 x - 21)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(2 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(2 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 3$ . This gives $LaTeX: \displaystyle -2[8 x^{2} \left(2 x + 3\right) -7 \cdot \left(2 x + 3\right)] = -2\left(2 x + 3\right) \left(8 x^{2} - 7\right)$ .