Factor LaTeX: \displaystyle - 50 x^{3} - 10 x^{2} + 50 x + 10 .

Factoring out the GCF LaTeX: \displaystyle -10 from each term gives LaTeX: \displaystyle -10(5 x^{3} + x^{2} - 5 x - 1) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(5 x + 1) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(5 x + 1) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 5 x + 1 . This gives LaTeX: \displaystyle -10[x^{2} \left(5 x + 1\right) -1 \cdot \left(5 x + 1\right)] = -10\left(5 x + 1\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -10\left(x - 1\right) \left(x + 1\right) \left(5 x + 1\right).