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\begin{center}
Math 101 - Final
\end{center}

Name \rule{5in}{.2pt}

\vspace{.1in}

Code Name \rule{5in}{.2pt}

\vspace{.1in}

Section Number \rule{5in}{.2pt}

\vspace{.1in}

\begin{enumerate}

\item  Sketch the graph of the equation 
and find its intersection with the $x$--axis.
\[
-3x+2y+4=0
\]
\vspace{3.1in}

\item Factor the polynomial $p(x)= 2x^2+10x-28$, and
solve the equation $p(x)=0$.
%\vspace{2.6in}
\newpage

\item  Compute and simplify
\[
\frac{16-x}{x^2-2x-8}+\frac{4}{x+2}-\frac{2}{x-4}
\]
\vspace{2.6in}

\item  Find the solutions of the equation
\[
2z^2+8z+9=0
\]
\vspace{2.6in}

\item   We have to build a rectangular patio such that
its width is 4 ft less than its length, and its total area is 117
square feet. What should be its length and width?
%\vspace{2.6in}
\newpage

\item  Find the equation of the line that goes through
the points $(0,5)$ and $(2,-1)$. Find the intersection of this
line with the horizontal line $y=1$.
\vspace{2.6in}

\item  Solve the system
\[
\left\{ 
\begin{array}{ccccccc}
 x &    &   & + & 4z & = & 0 \\
-x &  - & y & + & 2z & = & 2 \\
2x &  + & y & - & 3z & = & 1 
\end{array}
\right.
\]
\vspace{2.6in}

\item  If $g(x)=(3-x)x$ evaluate and simplify:
$g(5)$, $g(-2)$, $g(t+2)$.
\vspace{2.6in}

\item  Find the equation of the line through (2,-4) and (-10,1),
and find the distance between these points.
\vspace{2.6in}

\item  Simplify and factor:
\[
3y^2-(y-3(y^2-5))
\]
\vspace{2.6in}

\item  Simplify:
\[
\frac
{ \left( \frac{1}{y}-\frac{1}{x} \right) }
{ \left( \frac{1}{y^2}-\frac{1}{x^2} \right) }
\]
\vspace{2.6in}

\item Divide:
\[
\frac{2x^4+x^2-35}{x+2}
\]
\vspace{2.6in}

\item  Solve:
\[
\frac{4}{x+3}-\frac{5}{x-2}=6
\]
\vspace{2.6in}

\item  Rewrite using only positive exponents and simplify:
\[
(3x^2y^{-1})^2(4x^4y^{-3})^{-\frac{1}{2}}
\]
\vspace{2.6in}

\item  Rationalize the denominator and simplify:
\[
\frac{\sqrt{8}}{\sqrt{5}-3}
\]
\vspace{2.6in}

\item  Write the complex number in standard form $(a+bi)$:
\[
\frac{2-\sqrt{-16}}{1-2i}
\]
\vspace{2.6in}

\item  (10 points)  Solve and graph the inequality.
\[ -2 < \frac{2x-5}{2} \leq 2 \]
\vspace{2.6in}

\item  (10 points)  Solve the equation:
\[ |2x+2|=|5x-1| \]
\vspace{2.6in}

\item  (20 points)  Factor the polynomial.  (Hint: $(x-2)$ is a factor)
\[
x^3-7x+6
\]
\vspace{2.6in}

\item  (15 points)  You take a 12 mile hike.  
For the first 8 miles you travel at one speed.  
Then you pick up the pace and finish the next 4 miles 
2 miles per hour faster then the first 8 miles.  
The trip takes 9 hours.
How fast did you go in each part of the hike?











\end{enumerate}

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