Simple question regarding polynomials

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The discussion centers on the relationship between a polynomial k in variables x and y, and the condition k(x-1) = q, where q is also a polynomial in y. It is established that if k is not equal to zero, then q cannot be a polynomial solely in y, leading to the conclusion that k must equal zero for the equation to hold true. The participants explore the implications of polynomial division and the necessity of eliminating the x term to maintain the polynomial nature of q.

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