Factor $LaTeX: \displaystyle 20 x^{3} - 20 x^{2} - 35 x + 35$ .

Factoring out the GCF $LaTeX: \displaystyle 5$ from each term gives $LaTeX: \displaystyle 5(4 x^{3} - 4 x^{2} - 7 x + 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle 5[4 x^{2} \left(x - 1\right) -7 \cdot \left(x - 1\right)] = 5\left(x - 1\right) \left(4 x^{2} - 7\right)$ .