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Question Number 31542 by abdo imad last updated on 09/Mar/18
let p(x)=(1+x+x^2 )^n  −(1−x+x^2 )^n  ∈C[x]  1) find the roots of p(x)  2) factorize p(x) inside C[x].
$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{{n}} \:−\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{{n}} \:\in{C}\left[{x}\right] \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right]. \\ $$

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