Factor $LaTeX: \displaystyle 42 x^{3} + 54 x^{2} - 63 x - 81$ .

Factoring out the GCF $LaTeX: \displaystyle 3$ from each term gives $LaTeX: \displaystyle 3(14 x^{3} + 18 x^{2} - 21 x - 27)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(7 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(7 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 9$ . This gives $LaTeX: \displaystyle 3[2 x^{2} \left(7 x + 9\right) -3 \cdot \left(7 x + 9\right)] = 3\left(7 x + 9\right) \left(2 x^{2} - 3\right)$ .