Factor $LaTeX: \displaystyle - 16 x^{3} + 56 x^{2} + 18 x - 63$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(16 x^{3} - 56 x^{2} - 18 x + 63)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(2 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(2 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 7$ . This gives $LaTeX: \displaystyle -1[8 x^{2} \left(2 x - 7\right) -9 \cdot \left(2 x - 7\right)] = -\left(2 x - 7\right) \left(8 x^{2} - 9\right)$ .