Factor LaTeX: \displaystyle - 4 x^{3} - 40 x^{2} + 4 x + 40 .

Factoring out the GCF LaTeX: \displaystyle -4 from each term gives LaTeX: \displaystyle -4(x^{3} + 10 x^{2} - x - 10) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(x + 10) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(x + 10) . The polynomial now has a common binomial factor of LaTeX: \displaystyle x + 10 . This gives LaTeX: \displaystyle -4[x^{2} \left(x + 10\right) -1 \cdot \left(x + 10\right)] = -4\left(x + 10\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -4\left(x - 1\right) \left(x + 1\right) \left(x + 10\right).