Factor $LaTeX: \displaystyle 14 x^{3} + 42 x^{2} + 8 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(7 x^{3} + 21 x^{2} + 4 x + 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 7 x^{2}$ , gives $LaTeX: \displaystyle 7 x^{2}(x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 4$ , gives $LaTeX: \displaystyle 4(x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 3$ . This gives $LaTeX: \displaystyle 2[7 x^{2} \left(x + 3\right) +4 \cdot \left(x + 3\right)] = 2\left(x + 3\right) \left(7 x^{2} + 4\right)$ .