Factor $LaTeX: \displaystyle - 18 x^{3} + 54 x^{2} + 3 x - 9$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(6 x^{3} - 18 x^{2} - x + 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 3$ . This gives $LaTeX: \displaystyle -3[6 x^{2} \left(x - 3\right) -1 \cdot \left(x - 3\right)] = -3\left(x - 3\right) \left(6 x^{2} - 1\right)$ .