MeldHunter

Ahh dang, it seems its incorrect. Though it gave a hint, Define $P_n\left(x-\frac1x\right)=x^n-\frac1{x^n}$ for odd n and seek a recursive relationship between $P_{2k+1}$ and lower order polynomials.

Thanks again. I think I can fill in the gaps!

Thank you! I just really want the methods.

Thanks! 

Thanks! The detailed explanation really helps.