Factor $LaTeX: \displaystyle - 63 x^{3} + 27 x^{2} + 42 x - 18$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(21 x^{3} - 9 x^{2} - 14 x + 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(7 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(7 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 3$ . This gives $LaTeX: \displaystyle -3[3 x^{2} \left(7 x - 3\right) -2 \cdot \left(7 x - 3\right)] = -3\left(7 x - 3\right) \left(3 x^{2} - 2\right)$ .