Factor $LaTeX: \displaystyle 21 x^{3} - 27 x^{2} - 49 x + 63$ .

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