Factor $LaTeX: \displaystyle 3 x^{3} + 6 x^{2} + 6 x + 12$ .

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