Irreducible Polynomial/Examples/x^2 + 1 in Complex Numbers

Examples of Irreducible Polynomials
Consider the polynomial:
 * $\map P x = x^2 + 1$

over the ring of polynomials $\C \sqbrk X$ over the complex numbers.

Then $\map P x$ is not irreducible, as:
 * $x^2 + 1 \equiv \paren {x + i} \paren {x - i}$