Factor LaTeX: \displaystyle - 40 x^{3} - 45 x^{2} + 40 x + 45 .

Factoring out the GCF LaTeX: \displaystyle -5 from each term gives LaTeX: \displaystyle -5(8 x^{3} + 9 x^{2} - 8 x - 9) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(8 x + 9) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(8 x + 9) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 8 x + 9 . This gives LaTeX: \displaystyle -5[x^{2} \left(8 x + 9\right) -1 \cdot \left(8 x + 9\right)] = -5\left(8 x + 9\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -5\left(x - 1\right) \left(x + 1\right) \left(8 x + 9\right).