# 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:

$x^2 + 1 \equiv \paren {x + i} \paren {x - i}$