Hi I do not understand the splitting fields, for example in the following:
find splitting field of (x^4)+1 over Q. all I know is that this function factors to (x^2+i)(x^2-i) but how do we know that this is the the end? how do we know this cannot be more factorized.
and in these kind of questions (splitting a field) is it all I have to do? just to find the factors?