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The polynomials in $\Fb[x]$ are infinite. However, if we bound the degree, we find a finite set, as for example   $$S:=\{p \in \Fb[x] \vert \deg(p) < 3\}=\{0,1,x,x+1,x^2,x^2+x, x^2+1,x^2+x+1\}.$$  This set contains $8$ polynomials; indeed, $f \in S$ if and only if, if  $f$ is of the form $$f=a_0+a_1x+a_2x^2,\, a_0,a_1,a_2 \in\Fb$$  Since there are two choices for each coefficient $a_0,a_1,a_2 $ the polynomials are $2^3=8$.  If we take two polynomials $f,g $ in $ S$, then $f+g$ belongs to $S$ as well, since when we sum two polynomials, the degree cannot grow (see Exercise \ref{degree}), according to the rule in $\Fb[x]$