Answer
$x^{3}+2x^{2}+2x+4$
Work Step by Step
We start with two factors: $(x^{2}+2)(x+2)$
We then split one of the factors up, and multiply each part by the second factor. $x^{2}(x+2), 2(x+2)$
We then multiply the factors out. $(x^{3}+2x^{2}), (2x+4)$
Lastly we add the two parts together, leaving us with our polynomial. $x^{3}+2x^{2}+2x+4$
