I am trying to factor a polynomial into irreducible factors in and got it to the following stage:

I noticed that wolfram has it reduced even further by splitting into . I was just wondering how this was done? I understand how to split the using complex numbers; however, nothing occured to me in

Also, just out of interest, if you have an equation using the variable , for example, and you want to talk about it within the set of real numbers, is it correct to say or should you say ?