Factor $LaTeX: \displaystyle 16 x^{3} - 48 x^{2} + 18 x - 54$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(8 x^{3} - 24 x^{2} + 9 x - 27)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(x - 3)$ . 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 $LaTeX: \displaystyle 2[8 x^{2} \left(x - 3\right) +9 \cdot \left(x - 3\right)] = 2\left(x - 3\right) \left(8 x^{2} + 9\right)$ .