Simple question regarding polynomials

[slevvio]

Hello all I had a simple question that I am intuitively sure I know the answer to but can't quite prove it.

Suppose k is a polynomial in x and y, and k(x-1) = q for q some polynomial in y. Then is k = 0 ?

How do I verify that k must be equal to 0? I can see that to just get a polynomial in y we have to try to get rid of that x term, but I can't quite prove why we can't just make some polynomial that gets rid of it somehow.

any help would be appreciated, thanks

 

[gb7nash]

Suppose k != 0, so q = ...

 

[elegysix]

If k=0, then k(x-1)=q=0.

If you let a polynomial in y be P(y) then if k=P(y)/(x-1), q=P(y)...