Factor $LaTeX: \displaystyle 60 x^{3} - 60 x^{2} + 20 x - 20$ .

Factoring out the GCF $LaTeX: \displaystyle 20$ from each term gives $LaTeX: \displaystyle 20(3 x^{3} - 3 x^{2} + x - 1)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(x - 1)$ . 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 $LaTeX: \displaystyle 20[3 x^{2} \left(x - 1\right) +1 \cdot \left(x - 1\right)] = 20\left(x - 1\right) \left(3 x^{2} + 1\right)$ .