Factor $LaTeX: \displaystyle - 36 x^{3} + 8 x^{2} - 54 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(18 x^{3} - 4 x^{2} + 27 x - 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(9 x - 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(9 x - 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x - 2$ . This gives $LaTeX: \displaystyle -2[2 x^{2} \left(9 x - 2\right) +3 \cdot \left(9 x - 2\right)] = -2\left(9 x - 2\right) \left(2 x^{2} + 3\right)$ .