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