Factor $LaTeX: \displaystyle - 12 x^{3} + 4 x^{2} - 18 x + 6$ .

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