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**terrorsquid** I am trying to factor a polynomial into irreducible factors in $\displaystyle \mathbb{R}$ and got it to the following stage:

$\displaystyle (x-1)(x+1)(x^4+4) $

I noticed that wolfram has it reduced even further by splitting $\displaystyle x^4+4$ into $\displaystyle (2-2 x+x^2) (2+2 x+x^2)$. I was just wondering how this was done? I understand how to split the $\displaystyle x^4+4$ using complex numbers; however, nothing occured to me in $\displaystyle \mathbb{R}$

Also, just out of interest, if you have an equation using the variable $\displaystyle m$, for example, and you want to talk about it within the set of real numbers, is it correct to say $\displaystyle \mathbb{R} [x]$ or should you say $\displaystyle \mathbb{R} [m]$?