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p-x-x-2-x-1-n-x-2-x-1-n-1-roots-of-p-x-2-factorize-p-x-inside-C-x-




Question Number 146082 by mathmax by abdo last updated on 10/Jul/21
p(x)=(x^2 −x+1)^n −(x^2 +x+1)^n   1) roots of p(x)?  2) factorize p(x) inside C[x]
$$\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} −\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right)? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$

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