$$ f(y)=Ny(y-1)^2-y-y^{2N+3}+y^{N+1}\left (N^2y^3+(-2N^2+N+1)y^2+(N^2-2N)y+N+1 \right ) $$ where $N$ is an integer bigger or equal to 2, and $y>1$.How to show $f(y)<0$? Any hint? Thanks a lot.
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Eww, where did this polynomial come from? I'd start with the substitution $y=x+1$ and see if that leads anywhere... – user7530 Dec 22 '13 at 22:30
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Rewrite as $Ny(y-1)^2-y-y^{2N+3}+y^{N+1}(N^2y(y-1)^2+N(y-1)^2+1)$ for a start – Hagen von Eitzen Dec 22 '13 at 22:41
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I think we should factor out the $y$, as it does not change the sign. – benh Dec 22 '13 at 22:55
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@HagenvonEitzen: I think an $y^{N+3}$ is missing. – benh Dec 22 '13 at 23:06