Factor $LaTeX: \displaystyle - 30 x^{3} + 54 x^{2} - 5 x + 9$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(30 x^{3} - 54 x^{2} + 5 x - 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(5 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(5 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x - 9$ . This gives $LaTeX: \displaystyle -1[6 x^{2} \left(5 x - 9\right) +1 \cdot \left(5 x - 9\right)] = -\left(5 x - 9\right) \left(6 x^{2} + 1\right)$ .