Factor $LaTeX: \displaystyle - 54 x^{3} - 9 x^{2} + 42 x + 7$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(54 x^{3} + 9 x^{2} - 42 x - 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(6 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(6 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 6 x + 1$ . This gives $LaTeX: \displaystyle -1[9 x^{2} \left(6 x + 1\right) -7 \cdot \left(6 x + 1\right)] = -\left(6 x + 1\right) \left(9 x^{2} - 7\right)$ .