\chapter{Polynomial and rational functions}
\section{The Rational Zero Theorem}
Answer the questions in your own words.
\begin{enumerate}
\item Numbers such as \(1,-2,0,-3,8\) are called \textit{integers}.
What are numbers such as \(1/2, -3/5, 3/7\)
called?
\item What are numbers such as \(\sqrt{2}\), \(\pi\), \(\pi^2/3\) called?
\item
The polynomial \(x^2-7\) cannot be factored using integers. Does that mean that it cannot be
be factored at all?
\item
Neither \(x^2-7\) nor \(x^2+7\) can be factored using integers. But what is the difference
between the two cases?
\item What is a rational zero of a polynomial \(f(x)\)?
\item
What does the Rational Zero Theorem say?
\item
Suppose the degree of \(f(x)\) is \(3\) and its
possible rational zeros are \(\pm 1, \pm 4, \pm 7\). After
trying synthetic division with
\(x=1\) and \(x=-1\) without success, we find that \(x=4\) works. What is our next step?
\item
Suppose now that \(f(x)\) has degree \(4\) and the list of possible rational zeros is
\(\pm 1, \pm 2, \pm 3, \pm 6\). After trying \(x=1\), \(x=-1\), \(x=2\) without success, we find that
\(x=-2\) works. What is our next step?
\end{enumerate}