How to factorize bi-quadratic

Question

I came across this question and have no idea how to factorise this. How can $x^4+4$ be factorised?

Answer 1

Recall that the Quadratic Formula $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ solves $ax^2+bx+c=0$ just as $$x^2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ solves $ax^4+bx^2+c=0$.

Thus apply it for $a=1,b=0,c=4$

Answer 2

Here is how it can be factored in high school: $$x^4+4=(x^4+4x^2+4)-4x^2=(x^2+2)^2-(2x)^2=(x^2+2-2x)(x^2+2+2x).$$