Factor $LaTeX: \displaystyle 42 x^{3} + 54 x^{2} - 35 x - 45$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(7 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(7 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 9$ . This gives $LaTeX: \displaystyle 6 x^{2} \left(7 x + 9\right) -5 \cdot \left(7 x + 9\right) = \left(7 x + 9\right) \left(6 x^{2} - 5\right)$ .