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I am stuck in the following question :- $f(x, y)$ is a bivariate polynomial with coefficients in $Z$. We have to show that $deg(GCD(f, f_y)) > 0$ iff $deg(GCD(f, f_x)) > 0$.(Here $f_x$ denotes the partial derivative with respect to $x$.)

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Hint: Suppose that $h$ divides both $f$ and $f_x$. What can you say about the relation between $h$ and $f$? Hint 2: If $f$ is a one variable polynomial, do you know what it means when $h$ divides both $f$ and $f'$? –  David Speyer Apr 30 '12 at 17:40
    
@DavidSpeyer , thanks for the hint. Can you kindly elaborate on hint 1 ? That will be helpful. –  babu123 Apr 30 '12 at 18:00
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