Factor $LaTeX: \displaystyle - 14 x^{3} + 42 x^{2} - 18 x + 54$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(7 x^{3} - 21 x^{2} + 9 x - 27)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 7 x^{2}$ , gives $LaTeX: \displaystyle 7 x^{2}(x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 9$ , gives $LaTeX: \displaystyle 9(x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 3$ . This gives $LaTeX: \displaystyle -2[7 x^{2} \left(x - 3\right) +9 \cdot \left(x - 3\right)] = -2\left(x - 3\right) \left(7 x^{2} + 9\right)$ .