Constructing the field with eight elements

Write down an irreducible cubic polynomial over $F_{2}$ .
Construct a field with exactly eight elements and write down its multiplication table.

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L A T E X

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\begin{enumerate}[topsep=0.1in]
	\item Write down an irreducible cubic polynomial over ${\bf F}_2$.
	\item Construct a field with exactly eight elements and write down its multiplication table.
\end{enumerate}