You can use the fact that will divide , where are elements from your ring.
Applying this, also divides
You can try to draw a conclusion from this.
My task is to find the gcd of and .
Long division isn't giving me a clue here. My hunch is that the gcd is one, but I'm not sure I can prove that by showing they are irreducible (over what ring would I do that anyway? the question does not specify) or something like that.