Factor $LaTeX: \displaystyle 28 x^{3} + 42 x^{2} + 20 x + 30$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(14 x^{3} + 21 x^{2} + 10 x + 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 7 x^{2}$ , gives $LaTeX: \displaystyle 7 x^{2}(2 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(2 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 3$ . This gives $LaTeX: \displaystyle 2[7 x^{2} \left(2 x + 3\right) +5 \cdot \left(2 x + 3\right)] = 2\left(2 x + 3\right) \left(7 x^{2} + 5\right)$ .