Given that $x^n - (1/x^n)$ is expressible as a polynomial in $x - (1/x)$ with real coefficients only if $n$ is an odd positive integer, find $P(z)$ so that $P(x-(1/x)) = x^5 - (1/x)^5.$

I've tried $x^5+5x^3+5x$, but it isn't working :( Help greatly appreciated!

Question

Given that $x^n - (1/x^n)$ is expressible as a polynomial in $x - (1/x)$ with real coefficients only if $n$ is an odd positive integer, find $P(z)$ so that $P(x-(1/x)) = x^5 - (1/x)^5.$

I've tried $x^5+5x^3+5x$, but it isn't working :( Help greatly appreciated!

ganeshie8 · Answer

http://math.stackexchange.com/questions/1414792/find-a-polynomial-in-x-frac1x