Factor LaTeX: \displaystyle - 63 x^{3} - 72 x^{2} + 63 x + 72 .

Factoring out the GCF LaTeX: \displaystyle -9 from each term gives LaTeX: \displaystyle -9(7 x^{3} + 8 x^{2} - 7 x - 8) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(7 x + 8) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(7 x + 8) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 7 x + 8 . This gives LaTeX: \displaystyle -9[x^{2} \left(7 x + 8\right) -1 \cdot \left(7 x + 8\right)] = -9\left(7 x + 8\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -9\left(x - 1\right) \left(x + 1\right) \left(7 x + 8\right).