Given the polynomial
which has $a=\sqrt 3+\sqrt 5$ as one of its roots in $\Bbb C$, can you use $f(x)$ to construct a field $E$ of the form $Q[x]/I $ for some appropriate ideal $I$?
And does $f(x)$ factorize over this field $E$?
Any help would be appreciated thankyou!! :)
I know that f(x) is irreducible over Z_5 if that is useful.