I am not sure if I making some very fundamental mistake. But Gallian says that $2x^2+4$ is reducible over $\mathbb C$.
If $D$ be an integral domain. A polynomial $f(x)$ from $D[x]$ is said to be irreducible over $D$ if whenever $f(x)$ is expressed as a product $f(x)=g(x)h(x)~~|~~g(x),h(x) \in D[x]$, then $g(x)$ or $h(x)$ is a unit in $D[x]$
$2x^2+4= 2(x^2+2)$ and $2$ is clearly a unit in $\mathbb C$. Hence, it should be irreducible right?