deletions | additions       diff --git a/section_Bytes_The_polynomials_in__.tex b/section_Bytes_The_polynomials_in__.tex  index 5866b99..b835dfc 100644  --- a/section_Bytes_The_polynomials_in__.tex  +++ b/section_Bytes_The_polynomials_in__.tex 
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This set contains $8$ polynomials; indeed, $f \in S$ if and only 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 also  $f+g$ belongs to $S$ as well, $S$,  since when we sum two polynomials, the degree cannot grow (see Exercise \ref{degree}), according to the rule in $\Fb[x]$ $$\deg(f+g)\leq \deg(f), \deg(g); \qquad \deg(f+g)<\deg(f),\deg(g) \iff \deg(f)=\deg(g). $$  However, if we multiply $f,g$, their product $fg$ can be outside $S$; for example  $$