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\documentclass[12pt,thmsa]{article}
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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 11:07:11 1997}
%TCIDATA{CSTFile=Exam.cst}
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\input{tcilatex}
\begin{document}


\section{Exam}

\subsection{Text}

\section{Factoring}

\subsection{Problems}

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Setup}

Choice Space:\ 2

Choices:\ No Break, Radio Buttons, Permute

Question Space:1

Title:Factoring Exam

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

Conditions: $a\neq 0$

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)^{2}}{x^{2}+2xa+a^{2}}{expand}}
%BeginExpansion
x^{2}+2xa+a^{2}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-a)}{\left( x+a\right) \left( x-a\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-a\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x-a)^{2}}{\left( x-a\right) ^{2}}{evaluate}}
%BeginExpansion
\left( x-a\right) ^{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x+a)^{2}}{\left( x+a\right) ^{2}}{evaluate}}
%BeginExpansion
\left( x+a\right) ^{2}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x+2a)(x-a)}{\left( x+2a\right) \left( x-a\right) }{evaluate}}
%BeginExpansion
\left( x+2a\right) \left( x-a\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$n:=\limfunc{rand}(1,10)$

$d:=\func{rand}(2,10)$

$s:=\func{rand}\left( \left\{ -1,1\right\} \right) $

$a:=s\frac{n}{d}$

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)^{2}}{x^{2}+2xa+a^{2}}{expand}}
%BeginExpansion
x^{2}+2xa+a^{2}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-a)}{\left( x+a\right) \left( x-a\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-a\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x-a)^{2}}{\left( x-a\right) ^{2}}{evaluate}}
%BeginExpansion
\left( x-a\right) ^{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x+a)^{2}}{\left( x+a\right) ^{2}}{evaluate}}
%BeginExpansion
\left( x+a\right) ^{2}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x+2a)(x-a)}{\left( x+2a\right) \left( x-a\right) }{evaluate}}
%BeginExpansion
\left( x+2a\right) \left( x-a\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$b:=\limfunc{rand}(-5,5)$

Conditions: $\left( ab\neq 0\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)(x+b)}{x^{2}+xb+ax+ab}{expand}}
%BeginExpansion
x^{2}+xb+ax+ab%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x-b)}{\left( x-a\right) \left( x-b\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x-b\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-b)}{\left( x+a\right) \left( x-b\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-b\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x+b)}{\left( x+a\right) \left( x+b\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x+b\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x+b)}{\left( x-a\right) \left( x+b\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x+b\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

Conditions: $a\neq 0$

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)^{3}}{x^{3}+3ax^{2}+3xa^{2}+a^{3}}{expand}}
%BeginExpansion
x^{3}+3ax^{2}+3xa^{2}+a^{3}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x+a)^{2}(x-a)}{\left( x+a\right) ^{2}\left( x-a\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) ^{2}\left( x-a\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x-a)^{3}}{\left( x-a\right) ^{3}}{evaluate}}
%BeginExpansion
\left( x-a\right) ^{3}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{(x+a)^{3}}{\left( x+a\right) ^{3}}{evaluate}}
%BeginExpansion
\left( x+a\right) ^{3}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-a)^{2}}{\left( x+a\right) \left( x-a\right) ^{2}}{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-a\right) ^{2}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$n:=\limfunc{rand}(1,10)$

$d:=\func{rand}(2,10)$

$s:=\func{rand}\left( \left\{ -1,1\right\} \right) $

$b:=s\frac{n}{d}$

Conditions: $\left( a\neq 0\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)(x+b)}{x^{2}+xb+ax+ab}{expand}}
%BeginExpansion
x^{2}+xb+ax+ab%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x-b)}{\left( x-a\right) \left( x-b\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x-b\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-b)}{\left( x+a\right) \left( x-b\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-b\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x+b)}{\left( x+a\right) \left( x+b\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x+b\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x+b)}{\left( x-a\right) \left( x+b\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x+b\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$c:=\limfunc{rand}(-5,5)$

$n:=\limfunc{rand}(1,10)$

$d:=\func{rand}(2,10)$

$s:=\func{rand}\left( \left\{ -1,1\right\} \right) $

$b:=s\frac{n}{d}$

Conditions: $\left( ac\neq 0\right) \wedge \left( a\neq b\right) \wedge
\left( a\neq c\right) \wedge \left( b\neq c\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{
%\FORMULA{(x+a)(x+b)\left( x+c\right) }{x^{3}+x^{2}c+x^{2}b+xbc+ax^{2}+axc+abx+abc\allowbreak }{expand}}
%BeginExpansion
x^{3}+x^{2}c+x^{2}b+xbc+ax^{2}+axc+abx+abc\allowbreak %
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x-b)\left( x+c\right) }{\left( x-a\right) \left( x-b\right) \left( x+c\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x-b\right) \left( x+c\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-b)\left( x+c\right) }{\left( x+a\right) \left( x-b\right) \left( x+c\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-b\right) \left( x+c\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x+b)\left( x+c\right) }{\left( x+a\right) \left( x+b\right) \left( x+c\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x+b\right) \left( x+c\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x+b)(x+c)}{\left( x-a\right) \left( x+b\right) \left( x+c\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x+b\right) \left( x+c\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$b:=\limfunc{rand}(-5,5)$

Conditions: $\left( ab\neq 0\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(x+a)(x+\frac{b}{x})}{x^{2}+b+ax+a\frac{b}{x}}{expand}}
%BeginExpansion
x^{2}+b+ax+a\frac{b}{x}%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x-a)(x-\frac{b}{x})}{\left( x-a\right) \left( x-\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x-a\right) \left( x-\frac{b}{x}\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-\frac{b}{x})}{\left( x+a\right) \left( x-\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-\frac{b}{x}\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x+\frac{b}{x})}{\left( x+a\right) \left( x+\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x+\frac{b}{x}\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x-\frac{a}{x})(x+b)}{\left( x-\frac{a}{x}\right) \left( x+b\right) }{evaluate}}
%BeginExpansion
\left( x-\frac{a}{x}\right) \left( x+b\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$b:=\limfunc{rand}(-5,5)$

Conditions: $\left( ab\neq 0\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{
%\FORMULA{(x+\frac{a}{x})(x+\frac{b}{x})}{x^{2}+b+a+\frac{a}{x^{2}}b}{expand}}
%BeginExpansion
x^{2}+b+a+\frac{a}{x^{2}}b%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(x-\frac{a}{x})(x-\frac{b}{x})}{\left( x-\frac{a}{x}\right) \left( x-\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x-\frac{a}{x}\right) \left( x-\frac{b}{x}\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+a)(x-\frac{b}{x^{2}})}{\left( x+a\right) \left( x-\frac{b}{x^{2}}\right) }{evaluate}}
%BeginExpansion
\left( x+a\right) \left( x-\frac{b}{x^{2}}\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(x+\frac{a}{x})(x+\frac{b}{x})}{\left( x+\frac{a}{x}\right) \left( x+\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x+\frac{a}{x}\right) \left( x+\frac{b}{x}\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(x-\frac{a}{x})(x+\frac{b}{x})}{\left( x-\frac{a}{x}\right) \left( x+\frac{b}{x}\right) }{evaluate}}
%BeginExpansion
\left( x-\frac{a}{x}\right) \left( x+\frac{b}{x}\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(1,5)$

$b:=\limfunc{rand}(-5,5)$

$c:=\limfunc{rand}(1,5)$

$d:=\limfunc{rand}(-5,5)$

Conditions: $\left( abcd\neq 0\right) $

\subsection{Statement}

Factor $%
%TCIMACRO{\FORMULA{(ax+by)(cx+dy)}{ax^{2}c+axdy+bycx+by^{2}d}{expand}}
%BeginExpansion
ax^{2}c+axdy+bycx+by^{2}d%
%EndExpansion
$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{(cx+by)(ax+dy)}{\left( cx+by\right) \left( ax+dy\right) }{evaluate}}
%BeginExpansion
\left( cx+by\right) \left( ax+dy\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(ax-by)(cx-dy)}{\left( ax-by\right) \left( cx-dy\right) }{evaluate}}
%BeginExpansion
\left( ax-by\right) \left( cx-dy\right) %
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{(ax+by)(cx+dy)}{\left( ax+by\right) \left( cx+dy\right) }{evaluate}}
%BeginExpansion
\left( ax+by\right) \left( cx+dy\right) %
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{
%\FORMULA{(ax+by)(cx-dy)}{\left( ax+by\right) \left( cx-dy\right) }{evaluate}}
%BeginExpansion
\left( ax+by\right) \left( cx-dy\right) %
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\section{Question}

\subsection{\protect\vspace{1pt}Comment}

Solve a cubic equation by factoring into a linear and a quadratic.

\subsection{Setup}

$a:=\limfunc{rand}(-4,4)$

$b:=\limfunc{rand}(-4,4)$

Condition: $(ab\neq 0)$ \ \ \ \ \ \ \ \ \ \ [non-trivial root for the linear
part]

$c:=1$

$E:=\limfunc{rand}(-5,5)$

$d:=\limfunc{rand}(5,8)$

$f:=(ax+b)(cx^{2}+dx+E)$

Condition: $(d^{2}-4cE>0)$ [real roots for the quadratic part]

Condition: $\sqrt{d^{2}-4cE}\neq \left\lfloor \sqrt{d^{2}-4cE}\right\rfloor $
[A way to make sure that the roots are non-integral]

$R_{1}:=\left\{ -b/a,\left( -d+\sqrt{d^{2}-4cE}\right) /2,\left( -d-\sqrt{%
d^{2}-4cE}\right) /2\right\} $\ [The correct answer]

$R_{2}:=\left\{ b/a,\left( -d+\sqrt{d^{2}-4cE}\right) /2,\left( -d-\sqrt{%
d^{2}-4cE}\right) /2\right\} $

$R_{3}:=\left\{ -b/a,\left( d+\sqrt{d^{2}-4cE}\right) /2,\left( d-\sqrt{%
d^{2}-4cE}\right) /2\right\} $

$R_{4}:=\left\{ b/a,\left( -d+\sqrt{d^{2}-4cE}\right) /4,\left( -d-\sqrt{%
d^{2}-4cE}\right) /4\right\} $

Choices: Break

\subsection{Statement}

Find the roots of $%
%TCIMACRO{\FORMULA{f}{f}{expand}}
%BeginExpansion
f%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{R_{1}}{R_{1}}{evaluate}}
%BeginExpansion
R_{1}%
%EndExpansion
$\correctchoice{}

\item  $%
%TCIMACRO{\FORMULA{R_{2}}{R_{2}}{evaluate}}
%BeginExpansion
R_{2}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{R_{3}}{R_{3}}{evaluate}}
%BeginExpansion
R_{3}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{R_{4}}{R_{4}}{evaluate}}
%BeginExpansion
R_{4}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of these
\end{description}

\end{document}
