Factor LaTeX: \displaystyle 18 x^{3} - 63 x^{2} - 8 x + 28 .

Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle 9 x^{2} , gives LaTeX: \displaystyle 9 x^{2}(2 x - 7) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -4 , gives LaTeX: \displaystyle -4(2 x - 7) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 2 x - 7 . This gives LaTeX: \displaystyle 9 x^{2} \left(2 x - 7\right) -4 \cdot \left(2 x - 7\right) = \left(2 x - 7\right) \left(9 x^{2} - 4\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle \left(2 x - 7\right) \left(3 x - 2\right) \left(3 x + 2\right).