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].](https://www.tinkutara.com/question/Q31542.png)
$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{{n}} \:−\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{{n}} \:\in{C}\left[{x}\right] \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right]. \\ $$