# Is $$\displaystyle{x}^{{4}}+{4}$$ an irreducible polynomial?

Is ${x}^{4}+4$ an irreducible polynomial?
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${x}^{4}+4=\left({x}^{2}+2i\right)\cdot \left({x}^{2}-2i\right)$
$=\left(x-\left(1-i\right)\right)\cdot \left(x+\left(1-i\right)\right)\cdot \left(x-\left(1+i\right)\right)\cdot \left(x+\left(1+i\right)\right)$
$=\left(\left(x-1\right)+i\right)\cdot \left(\left(x-1\right)-i\right)\cdot \left(\left(x+1\right)-i\right)\cdot \left(\left(x+1\right)+i\right)$
$=\left({\left(x-1\right)}^{2}+1\right)\cdot \left({\left(x+1\right)}^{2}+1\right)$
Reducible.