Factor LaTeX: \displaystyle - 10 x^{3} + 5 x^{2} + 10 x - 5 .

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