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\begin{document}
\begin{center}
{\textbf{\Large Math 010 Practice Problems for Test 3 Fall 2022}}
\end{center}
\begin{singlespacing}
The following are examples of potential exam questions. It is recommended that you show all work while doing these problems. No problem requires a calculator but you are welcome to use one.

\begin{enumerate}

\item 
Addition and subtraction with polynomials\\
Examples:
\begin{enumerate}


\item Simplify $(7y^2-2y+9)+(2y^2-3y+2)$

\vspace{3cm}


\item Simplify $(7y^2-2y+9)-(2y^2-3y+2)$

\vspace{3cm}

\item Simplify $(2x^3+3)+(17x^2-3x+4)$

\vspace{3cm}

\item Simplify $(3x^3+2x^2+4)-(3x^2+4x-2)$

\vspace{3cm}

\end{enumerate}

\item 
Multiplication with polynomials\\
Examples:
\begin{enumerate}
	
\item Simplify $(5x)(2y)$

\vspace{3cm}

\item Simplify $(x+1)^2$

\vspace{3cm}

\item Simplify $(5x+3)(2x-2)$

\vspace{3cm}

\item Simplify $(x+1)(x^2+3x+1)$

\vspace{3cm}

\item Simplify $(4x+2)(3x^2-2x-2)$

\vspace{3cm}
\end{enumerate}

\item 
Evaluate polynomials\\
Examples:
For the function $f(x)=x^2-6x+5$
\begin{enumerate}


\item Find $f(1)$
\vspace{3cm}

\item Find $f(-2)$
\vspace{3cm}

\item Find $f(5)$
\vspace{3cm}

\end{enumerate}

\item 
Graph of a polynomial\\
Examples:
\begin{enumerate}
\item Find the polynomial that makes this graph.

\includegraphics[scale=.5]{1,-1,-2 roots.png}

\item Find the polynomial that makes this graph.

\includegraphics[scale=.5]{-2,2,-3,1 roots.png}
\end{enumerate}

\item 
Add and subtract complex numbers\\
Examples:
\begin{enumerate}
\item Compute $\sqrt{-12}+\sqrt{-27}$
\vspace{5cm}
\item Compute $\sqrt{-8}+\sqrt{-32}$
\vspace{5cm}
\item Compute $\sqrt{-3}-\sqrt{-27}$
\vspace{5cm}
\item Compute $\sqrt{-8}-\sqrt{-2}$
\vspace{5cm}
\end{enumerate}


\item 
Multiply and divide complex numbers\\
Examples:
\begin{enumerate}
\item Compute $(3+2i)(4-3i)$
\vspace{5cm}
\item Compute $(5-3i)^2$
\vspace{5cm}
\item Compute $\frac{4+3i}{3-4i}$
\vspace{5cm}
\item Compute $\frac{4}{1-4i}$
\vspace{5cm}
\end{enumerate}

\item 
Factoring\\
Examples:
\begin{enumerate}
\item Factor $x^2+10x+24$
\vspace{5cm}
\item Factor $x^2-4$ 
\vspace{5cm}
\item Factor $10x^2-55x+70$
\vspace{5cm}
\item Factor $16x^2-32x+12$ 
\vspace{5cm}
\end{enumerate}

\item 
Solve quadratic equations\\
Examples:
\begin{enumerate}
\item Solve $5x^2=80$
\vspace{5cm}
\item Solve $x^2+4=0$
\vspace{5cm}
\item Solve $2x^2+9x-5=0$
\vspace{5cm}
\item Solve $4x^2-2x=-8$
\vspace{5cm}

\end{enumerate}


\end{enumerate}
\end{singlespacing}
\end{document}
