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Find all irreducible polynomials of the form [itex]x^2 + ax +b [/itex], where a,b belong to the field [itex]\mathbb{F}_3[/itex] with 3 elements.

Show explicitly that [itex]\mathbb{F}_3(x)/(x^2 + x + 2)[/itex] is a field by computing its multiplicative monoid.

Identify [[itex]\mathbb{F}_3(x)/(x^2 + x + 2)[/itex]]* as an abstract group.

any suggestions please?

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# Irreducible polynomials

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