quick question: does the irreducibility of a polynomial in a field depend on whether there are roots in it, or whether you can write it as the product of 2 polynomials with coefficients in the root, because I want to know if $x^4-2$ is irreducible in Q($2^{1/2}$), and I know there aren't roots in it, but can't you also write it as ($x^2 + $2^{1/2}$)($x^2 - $2^{1/2}$)
