Factor LaTeX: \displaystyle - 4 x^{3} + 9 x^{2} + 4 x - 9 .

Factoring out the GCF LaTeX: \displaystyle -1 from each term gives LaTeX: \displaystyle -(4 x^{3} - 9 x^{2} - 4 x + 9) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(4 x - 9) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(4 x - 9) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 4 x - 9 . This gives LaTeX: \displaystyle -1[x^{2} \left(4 x - 9\right) -1 \cdot \left(4 x - 9\right)] = -\left(4 x - 9\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -\left(x - 1\right) \left(x + 1\right) \left(4 x - 9\right).