Simple question regarding polynomials

  1. 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 cant just make some polynomial that gets rid of it somehow.

    any help would be appreciated, thanks
     
  2. jcsd
  3. gb7nash

    gb7nash 805
    Homework Helper

    Suppose k != 0, so q = ...
     
  4. 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)....
     
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