Factor $LaTeX: \displaystyle 63 x^{3} + 9 x^{2} - 14 x - 2$ .

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