Factor LaTeX: \displaystyle - 35 x^{3} + 35 x^{2} + 35 x - 35 .

Factoring out the GCF LaTeX: \displaystyle -35 from each term gives LaTeX: \displaystyle -35(x^{3} - x^{2} - x + 1) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(x - 1) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -1 , gives LaTeX: \displaystyle -1(x - 1) . The polynomial now has a common binomial factor of LaTeX: \displaystyle x - 1 . This gives LaTeX: \displaystyle -35[x^{2} \left(x - 1\right) -1 \cdot \left(x - 1\right)] = -35\left(x - 1\right) \left(x^{2} - 1\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -35\left(x - 1\right)^{2} \left(x + 1\right).