Does the polynomial $z^{n+1} + w^{n+1}$ factor as $(z^n + w^n)f(z,w)$?

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Does the complex polynomial $z^{n+1} + w^{n+1}$ factor as $(z^n + w^n)f(z,w)$? I don’t have any conditions on $f$ apart from that it must be continuous. If the answer is yes, I would appreciate information on how I can obtain $f$.