.I just need a counter example for each of theses problems, they have been killing me for a few days now..
A) The gcd of
, so the gcd is , up to a constant, and thus your answer is correct, though perhaps not the prettiest one.
B) If is a field in is a non constant polynomial having no roots in , then is irreducible in
has no roots over , but it is terribly NOT irreducible...
These are both false, but Everything i try works for them...