Factor $LaTeX: \displaystyle 27 x^{3} - 63 x^{2} - 15 x + 35$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(3 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(3 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 7$ . This gives $LaTeX: \displaystyle 9 x^{2} \left(3 x - 7\right) -5 \cdot \left(3 x - 7\right) = \left(3 x - 7\right) \left(9 x^{2} - 5\right)$ .