\Question{Polynomial Practice}
\begin{Parts}
\Part If $f$ and $g$ are non-zero real polynomials, how many roots do the following
polynomials have at least? How many can they have at most?
(Your answer may depend on the degrees of $f$ and $g$.)
\begin{enumerate}[(i)]
\item $f + g$
\item $f\cdot g$
\item $f/g$, assuming that $f/g$ is a polynomial
\end{enumerate}
\Part Now let $f$ and $g$ be polynomials over $\mathrm{GF}(p)$.
\begin{enumerate}[(i)]
\item If $f\cdot g = 0$, is it true that either $f=0$ or $g=0$?
\item If $\deg{f} \geq p$, show that there exists a polynomial $h$ with
$\deg{h} < p$ such that $f(x) = h(x)$ for all $x \in \{0,1,...,p-1\}$.
\item How many $f$ of degree \textit{exactly} $d