%Factoring Expressions and Solving Equations
%If you modify this file, please indicate here and in the footnote.
%Math263A

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\begin{center}
{\Large
Factoring Expressions and Solving Equations\footnote{
Copyright \copyright 2002, Larry Snyder and Todd Young.
All rights reserved.  Please address comments to young@math.ohiou.edu.}}
\end{center}

\begin{enumerate}
\item At the prompt, type the following commands and
         press \fbox{Enter}: \\
    \verb&   clear & \\
    \verb&   syms x &  \\
    \verb&   expr1 = (x-1)*(x-2)*(x-3)*(x-4)*(x-5) & \\
    \verb&   expr2 = expand(expr1) & \\
    \verb&   factor(expr2) &\\
    \verb&   solve(expr2) &  \dotfill This solves the equation $expr2 = 0$\\
    Explain what happened. What is the relationship
                  between solving and factoring?

\item Type and enter: \\
  \verb&   expr3 = x^4 + 3*x^3 + 3*x^2 + x + 3& \\
  \verb&   factor(expr3) & \\
  \verb&   solve(expr3) & \\
  \verb&   double(ans) & \\
  Explain what happened. Explain why an exact, symbolic
                 solution may not be as useful as an approximation.

\item Try to solve $expr3 - 3$ by typing the following commands: \\
    \verb&   factor(expr3 - 3) &\\
    \verb&   solve(expr3 - 3) &\\
    \verb&   double(ans) & \\
    Why is the answer so nice?

\item Make $expr4$ be equal to $expr1 + 1$ by typing: 
	\verb$ expr4 = expr1 + 1$ \\
   Try to factor $expr4$ by typing: \verb& factor(expr4)& \\
   And to solve $expr4 = 0$ by typing: \verb& solve(expr4)& \\
   Why do you think \textsc{MatLab} produces a numerical solution 
   (for \verb&solve&), rather than symbolic? Hint: Is 
   it possible in this case to
   give a symbolic solution? Why?

\item Prepare a brief (\verb$< $1 page) written report answering all 
      the questions. Use complete sentences and standard mathematical notation. 
      Do {\bf not} get a printout.

\end{enumerate}

\vfill 
\noindent
\textsf{The user learns basic algebraic manipulation commands
and is led to consider the difference between numerical and symbolic
solving techniques. The user must confront the foundational fact 
that a symbolic solution is not always possible.} 

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