Factor $LaTeX: \displaystyle 30 x^{3} - 30 x^{2} - 20 x + 20$ .

Factoring out the GCF $LaTeX: \displaystyle 10$ from each term gives $LaTeX: \displaystyle 10(3 x^{3} - 3 x^{2} - 2 x + 2)$ . 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, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle 10[3 x^{2} \left(x - 1\right) -2 \cdot \left(x - 1\right)] = 10\left(x - 1\right) \left(3 x^{2} - 2\right)$ .