\chapter{Polynomial and rational functions}
\section{Division of polynomials}
Answer the questions in your own words.
\begin{enumerate}
\item We divided the polynomial \(f(x)\) by \(x-c\), and found as answer
\[ \frac{f(x)}{x-c}=2x^2-5x+7+\frac{3}{x-c}.\] What is \(2x^2-5x+7\) called?
\item We divided the polynomial \(f(x)\) by \(x+c\), and found as answer
\[ \frac{f(x)}{x+c}=x^3-2-\frac{1}{x+c}.\] What is the degree of \(f(x)\)?
\item If we divide \(7x^3-3x^2+x+8\) by \(x-c\), what is the degree of the quotient?
\item We want to divide \(2x^3-x^2+4x+7\) by \(x^2-3\). Can we do it with synthetic division?
\item We divided \(f(x)\) by \(x^4-5\) and found as answer
\[\frac{f(x)}{x^4-5}=x+\frac{x^3-3x^2+7x+9}{x^4-5}.\]
What is \(x^3-3x^2+7x+9\) called?
\item We divided \(f(x)\) by \(x^3+x^2+x+1\) and found as answer
\[\frac{f(x)}{x^3+x^2+x+1}=x^2-x+1+\frac{3x^2+7x+9}{x^3+x^2+x+1}.\]
What is the degree of \(f(x)\)?
\item Suppose \(f(x)=(3x^2-5x+7)(2x^2-7)+3x-4\).
If we divide \(f(x)\) by \(2x^2-7\), what is the answer?
\item Suppose \(f(x)\) is a polynomial, and
\[ \frac{f(x)}{3x^2-9x+8}=5x^3+8x-3+\frac{x^2+1}{3x^2-9x+8}.\]
If we divide \(f(x)\) by \(3x^2-9x+8\) using long division, is the remainder going to be \(x^2+1\)?
\end{enumerate}