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Question: is polynomial irreducible in let be the ideal of...

Question details

Is polynomial 1+x+x^2 irreducible in \mathbb{Z}_5[x]? Let [1+x+x^2 ] be the ideal of \mathbb{Z}[x] generated by 1+x+x^2 . Is the quotient ring \mathbb{Z}/[1+x+x^2] a field? How many elements does the quotient ring ring \mathbb{Z}_5[x]/[1+x+x^2] have? Do the same for polynomial 1+x+x^3 in \mathbb{Z}_2[x].

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