90

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>90</B></div> <div> <B>Descomposición factorial</B></div> <div> <B>Factor común</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>P r o c e d i m i e n t o :</B></div> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se identifica el factor común </FONT></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se divide cada término del polinomio por el factor común</FONT></div> <div> <B>3.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se abren dos paréntesis, en el primero se escribe el factor común y en el segundo los cocientes hallados en el paso anterior (cada uno con su respectivo signo).</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados y enlaces a las soluciones de los problemas del Ejercicio 90</B></div> <bR> <div> <B>S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los treinta y dos problemas del Ejercicio 90:</FONT></div> <div> <B>F</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >actorar o descomponer en dos factores:</FONT></div> <bR> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="7db9a0190.gif" border=0 width="160" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#1" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/dSF-jvfdcKw" TARGET="_top" TITLE="https://youtu.be/dSF-jvfdcKw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >       <IMG SRC="7dbaa0190.gif" border=0 width="160" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#2" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/dSF-jvfdcKw" TARGET="_top" TITLE="https://youtu.be/dSF-jvfdcKw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >       <IMG SRC="7dbba1190.gif" border=0 width="161" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#3" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/dSF-jvfdcKw" TARGET="_top" TITLE="https://youtu.be/dSF-jvfdcKw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >       <IMG SRC="7dbcac180.gif" border=0 width="172" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#4" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/a0iy1H0gh8A" TARGET="_top" TITLE="https://youtu.be/a0iy1H0gh8A"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > </FONT></div> <div> <IMG SRC="7dbdb4180.gif" border=0 width="180" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#5" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/a0iy1H0gh8A" TARGET="_top" TITLE="https://youtu.be/a0iy1H0gh8A"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dbe93190.gif" border=0 width="147" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#6" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/a0iy1H0gh8A" TARGET="_top" TITLE="https://youtu.be/a0iy1H0gh8A"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dbf89180.gif" border=0 width="137" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#7" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0sXpZwS31kw" TARGET="_top" TITLE="https://youtu.be/0sXpZwS31kw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dc09f1f0.gif" border=0 width="159" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/cLzi8Qj3zqo" TARGET="_top" TITLE="https://youtu.be/cLzi8Qj3zqo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dc1c01c0.gif" border=0 width="192" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/cLzi8Qj3zqo" TARGET="_top" TITLE="https://youtu.be/cLzi8Qj3zqo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dc2a11c0.gif" border=0 width="161" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/cLzi8Qj3zqo" TARGET="_top" TITLE="https://youtu.be/cLzi8Qj3zqo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dc3b11c0.gif" border=0 width="177" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/rxPfuQGnmRI" TARGET="_top" TITLE="https://youtu.be/rxPfuQGnmRI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>      <IMG SRC="7dc4b81c0.gif" border=0 width="184" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/rxPfuQGnmRI" TARGET="_top" TITLE="https://youtu.be/rxPfuQGnmRI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dc5f71c0.gif" border=0 width="247" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/rxPfuQGnmRI" TARGET="_top" TITLE="https://youtu.be/rxPfuQGnmRI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dc60f1f0.gif" border=0 width="271" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/N4Hv4ChJ76I" TARGET="_top" TITLE="https://youtu.be/N4Hv4ChJ76I"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dc7e41c0.gif" border=0 width="228" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/N4Hv4ChJ76I" TARGET="_top" TITLE="https://youtu.be/N4Hv4ChJ76I"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><IMG SRC="7dc8dc1c0.gif" border=0 width="220" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/N4Hv4ChJ76I" TARGET="_top" TITLE="https://youtu.be/N4Hv4ChJ76I"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >       <IMG SRC="7dc9e81c0.gif" border=0 width="232" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#17" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0sXpZwS31kw" TARGET="_top" TITLE="https://youtu.be/0sXpZwS31kw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >       <IMG SRC="7dcadc1c0.gif" border=0 width="220" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#18" TITLE="90"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0sXpZwS31kw" TARGET="_top" TITLE="https://youtu.be/0sXpZwS31kw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > </FONT></div> <div> <IMG SRC="7dcbf41f0.gif" border=0 width="244" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/z6vqdk6g4ho" TARGET="_top" TITLE="https://youtu.be/z6vqdk6g4ho"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dccdc1c0.gif" border=0 width="220" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/z6vqdk6g4ho" TARGET="_top" TITLE="https://youtu.be/z6vqdk6g4ho"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dcdf31f0.gif" border=0 width="243" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/z6vqdk6g4ho" TARGET="_top" TITLE="https://youtu.be/z6vqdk6g4ho"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dce0c1c0.gif" border=0 width="268" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/2qlvUq2ZUww" TARGET="_top" TITLE="https://youtu.be/2qlvUq2ZUww"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dcf171c0.gif" border=0 width="279" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/2qlvUq2ZUww" TARGET="_top" TITLE="https://youtu.be/2qlvUq2ZUww"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd00b1c0.gif" border=0 width="267" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/2qlvUq2ZUww" TARGET="_top" TITLE="https://youtu.be/2qlvUq2ZUww"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dd10b1c0.gif" border=0 width="267" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/OARFI5CCTpQ" TARGET="_top" TITLE="https://youtu.be/OARFI5CCTpQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd2ec1f0.gif" border=0 width="236" height="31" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/OARFI5CCTpQ" TARGET="_top" TITLE="https://youtu.be/OARFI5CCTpQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd33d1c0.gif" border=0 width="317" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/OARFI5CCTpQ" TARGET="_top" TITLE="https://youtu.be/OARFI5CCTpQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dd4101c0.gif" border=0 width="272" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/-pRFmMdkB0s" TARGET="_top" TITLE="https://youtu.be/-pRFmMdkB0s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd5e41c0.gif" border=0 width="228" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/-pRFmMdkB0s" TARGET="_top" TITLE="https://youtu.be/-pRFmMdkB0s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd6ed1c0.gif" border=0 width="237" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/-pRFmMdkB0s" TARGET="_top" TITLE="https://youtu.be/-pRFmMdkB0s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="7dd7371c0.gif" border=0 width="311" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/Gha86MXVCUQ" TARGET="_top" TITLE="https://youtu.be/Gha86MXVCUQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="7dd89d1c0.gif" border=0 width="413" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/Gha86MXVCUQ" TARGET="_top" TITLE="https://youtu.be/Gha86MXVCUQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Soluciones de los problemas del Ejercicio 90</B></div> <bR> <div>  <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo1WvnjgMvl4wOQCEGhOSW7R" frameborder="0" allowfullscreen></iframe>  </div> <bR> <div> <B>F</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >actorar o descomponer en dos factores:</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="5cad44dc0.gif" border=0 width="324" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="5cae41dc0.gif" border=0 width="321" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="5caf40dc0.gif" border=0 width="320" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="5cb057dc0.gif" border=0 width="343" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="5cb169dc0.gif" border=0 width="361" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="5cb27cdc0.gif" border=0 width="636" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="7db8fbdc0.gif" border=0 width="763" height="220" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <IMG SRC="5cf6cc7c0.gif" border=0 width="716" height="124" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" 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