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\item $(x^3+x^2+x)+(x^4+x^3)$  \item $(x^2+x+1)+(x^2+x)$  \end{itemize}  Give your comments on the degree of $f\cdot g$ and $f+g$, with $f,g \in \Fb[x]$   and prove them. \Fb[x]$.  \end{Exercise}  As %  Since  we explained for multiples, can multiply polynomials,  we canunderline that  also "raising raise them  to powers" is   an operation powers,  withpeculiar properties, making this process different from  the analogous for polynomials over $\RR$. usual meaning  $$  f^n=\underbrace{f\cdots f}_n  $$  \\  Consider for example the polynomial $f(x)=x+1\in \Fb[x]$ and suppose to compute   its square power $(x+1)^2$. This means multiplying $f$ by itself so