<s>[INST] Given that $P(x)$ is a polynomial such that $P(x^2+1) = x^4+5x^2+3$, what is $P(x^2-1)$? How would I go about solving this? I can't find a clear relation between $x^2+1$ and $x^4+5x^2+3$ to solve $P(x^2-1)$.
 [/INST] Since$$x^4+5x^2+3=(x^2+1)^2+3(x^2+1)-1,$$ $P(x)=x^2+3x-1$ and therefore $P(x^2-1)=\cdots$
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