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\author{Berger42}
\pdfinfo{
  /Title (math-m03-quiz-2.pdf)
  /Creator (Cheatography)
  /Author (Berger42)
  /Subject (Math M03 Quiz \#2 Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Math M03 Quiz \#2 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Berger42} via \textcolor{DarkBackground}{\uline{cheatography.com/77212/cs/19125/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Berger42 \\
  \uline{cheatography.com/berger42} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 16th March, 2019.\\
   Updated 21st March, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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% from this page to resize cheat sheet text:
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.43873 cm} x{2.53827 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Dealing With Indexes}}  \tn
% Row 0
\SetRowColor{LightBackground}
If Odd & then nothing happens \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
If  Even & then use absolute value  bars \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
If term power is even and index is odd & then use absolute bars if answer is negative \tn 
% Row Count 6 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Put absolute value bars on variables}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{FOIL Method}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552770802_Annotation 2019-03-16 141252666.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Complex Fractions}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Simplify the numerator and the denominator of the complex fraction so that each is a single fraction. \newline % Row Count 3 (+ 3)
Perform the indicated division by multiplying the numerator of the complex fraction by the reciprocal of the denominator of the complex fraction. \newline % Row Count 6 (+ 3)
 Simplify if possible.% Row Count 7 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Greatest common Factor}}  \tn
% Row 0
\SetRowColor{LightBackground}
letters: each term has to have one & Numbers: the highest number all of terms can multiply into \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{letters:Chose the one with the lowest exponent} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factoring x\textasciicircum{}2\textasciicircum{}+bx+c}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Find a 2 numbers whose sum is b and products of c} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{More factoring}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{1. 3xy-4x-12y+16 \newline % Row Count 1 (+ 1)
2. x(3y-4) 4(3y-4) \newline % Row Count 2 (+ 1)
3.(3y-4)(x-4)% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{*Between 1\&2: factor first 2 terms and last 2 terms separately \newline Between 2\&3: remove the numbers on the outside and put them in parenthesis}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Exponents}}  \tn
% Row 0
\SetRowColor{LightBackground}
(a\textasciicircum{}n\textasciicircum{})\textasciicircum{}m\textasciicircum{}=a\textasciicircum{}n+m\textasciicircum{} & a\textasciicircum{}m\textasciicircum{}/a\textasciicircum{}n\textasciicircum{}=a\textasciicircum{}m-n\textasciicircum{} \tn 
% Row Count 1 (+ 1)
% Row 1
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a\textasciicircum{}0\textasciicircum{}=1 & a\textasciicircum{}-n\textasciicircum{}=1/a\textasciicircum{}n\textasciicircum{} \tn 
% Row Count 2 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Equations and Graphs 2}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552771968_Annotation 2019-03-16 140944.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.89126 cm} x{3.08574 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Rational  expressions}}  \tn
% Row 0
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Multiplication & Factor denominator, mutliply, reduce \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Divison & flip 2nd equation and multiply \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Unlike denominators + \& - & Factor denominator, Find LCD,simplify top \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{x+2/x\textasciicircum{}2\textasciicircum{} + x - 42 {\emph{ x+7/x\textasciicircum{}2\textasciicircum{} - 4 \newline  \newline x+2/(x-6)(x+7) }} x+7/(x-2)(x+2) \newline x-2/x-6 \newline  \newline 8/x-2+x - 6/x\textasciicircum{}2\textasciicircum{}-4+2/x+2 \newline  \newline 8/x-2+x - 6/(x+2)(x-2)+2/x+2 \newline  \newline 8+x-6+2 \newline x-16}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Rational function}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{f(x)=p(x)/q(x)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Solve it like a function} \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Finding domain:  \newline Demoninator=0 \newline Solve  \newline Those values are the excluded values \newline Solve the rest of the equation \newline if you get the excluded value your answer is no real solution}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{MORE Factoring}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552772523_Annotation.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Equations And Graphs}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552771867_Annotation 2019-03-16 140817.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.32733 cm} x{1.60195 cm} x{1.64772 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Special case and FACTORING}}  \tn
% Row 0
\SetRowColor{LightBackground}
 & 1.(a+b)(a-b)= a\textasciicircum{}2\textasciicircum{}-b\textasciicircum{}2\textasciicircum{} &  \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Perfect  Square Trinomial & 2. (a+b)\textasciicircum{}2\textasciicircum{}= a\textasciicircum{}2\textasciicircum{}+2ab+b\textasciicircum{}2\textasciicircum{} & 4. (a-b)\textasciicircum{}2\textasciicircum{}= a\textasciicircum{}2\textasciicircum{}-2ab+b\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Sum \& Difference of Cubes & 3.a\textasciicircum{}3\textasciicircum{}-b\textasciicircum{}3\textasciicircum{}= (a-b)(a\textasciicircum{}2\textasciicircum{}+ab+b\textasciicircum{}2\textasciicircum{} & 5.a\textasciicircum{}3\textasciicircum{}+b\textasciicircum{}3\textasciicircum{}= (a+b)(a\textasciicircum{}2\textasciicircum{}-ab+b\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
Difference of Square & 6.(a- b)\textasciicircum{}2\textasciicircum{}= (a-b)(a+b) &  \tn 
% Row Count 10 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Solving with Scientific notation}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{separate between the operation for each term then solve each, then combine% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{(2x10\textasciicircum{}3\textasciicircum{})(1.8x10\textasciicircum{}-7\textasciicircum{}) \newline  \newline 2x1.8=3.6 \newline  \newline 10\textasciicircum{}3\textasciicircum{}x10\textasciicircum{}-7\textasciicircum{}=10\textasciicircum{}-4\textasciicircum{} \newline {\bf{Answer:}} 3.6x10\textasciicircum{}-4\textasciicircum{}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factoring trinomials 2}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552771143_Annotation 2019-03-16 141252666.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factoring Trinomials}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552771108_Annotation 2019-03-16 141252666.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
f(x)=x+4 when x=4-\textgreater{} & solve by replacing the x with the one inside  the f() \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Graphing}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{it'll ask  for you  to solve the equation then graph your solutions, they should be x% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Solving f(x)}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/berger42_1552769631_Examples+a.+f(g(x))+b.+g(f(x))+Plug+in+equation+Plug+in+equation.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Replace the x in the equation (next to the letter) with the equation that comes after the equal sign}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Rational equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Factor Denominators find excluded values} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Find LCD of all terms multiply by LCD} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{check solution} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{*always  have at least 1 fraction}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}