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

Factoring out the GCF $LaTeX: \displaystyle 6$ from each term gives $LaTeX: \displaystyle 6(9 x^{3} - 9 x^{2} - 7 x + 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle 6[9 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = 6\left(x - 1\right) \left(9 x^{2} - 7\right)$ .