Question Number 34669 by math khazana by abdo last updated on 09/May/18
![let P(x)=(1+x+ix^2 )^n −(1+x −ix^2 )^n 1) find the roots of P(x) 2) factorize inside C[x] P(x) 3) factorize indide R[x] P(x).](https://www.tinkutara.com/question/Q34669.png)
$${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{x}+{ix}^{\mathrm{2}} \right)^{{n}} \:−\left(\mathrm{1}+{x}\:−{ix}^{\mathrm{2}} \right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{P}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{indide}\:{R}\left[{x}\right]\:{P}\left({x}\right). \\ $$
Commented by math khazana by abdo last updated on 09/May/18
$${n}\:{integr}\:{natural} \\ $$