113

<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>113</B></div> <div> <B>M á x i m o   c o m ú n   d i v i s o r</B></div> <div> <B>Máximo común divisor de dos polinomios por divisiones sucesivas</B></div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:728px;height:90px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="5388515922"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>Procedimiento</B></div> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se ordenan los polinomios con relación a una misma letra</FONT></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Si es posible, se factorizan los polinomios; los factores comunes a ambos polinomios harán parte del m.c.d.</FONT></div> <div> <B>3.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se divide el polinomio de mayor grado entre el de menor grado</FONT></div> <div> <B>4.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Si la división es exacta, el divisor es el m.c.d.</FONT></div> <div> <B>5.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Si la división no es exacta, se divide el divisor por el primer residuo, éste por el segundo residuo y así sucesivamente hasta llegar a una división exacta</FONT></div> <div> <B>6.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  El último divisor es el m.c.d. buscado</FONT></div> <div> <I>Nota1:</I><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><I> todas las divisiones deben continuarse hasta que el primer término del residuo sea de grado inferior al primer término del divisor</I></FONT></div> <div> <I>Nota2:</I><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><I> durante el proceso, se puede dividir o multiplicar el dividendo, o el divisor o el residuo por un factor cualquiera.</I></FONT></div> <div> <FONT SIZE="4" COLOR="#009900" FACE="Bell MT" ><U>Nota3</U>:</FONT> la simbología para denotar el m.c.d., <I>k</I>, de los números <I>a</I>, <I>b</I>, ... es la siguiente:</div> <DIV ALIGN="LEFT"></DIV> <div> (<I>a</I>, <I>b</I>, ...) = <I>k</I><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >.</FONT></div> <bR> <div> <B>Enunciados y enlaces a las soluciones de los problemas del Ejercicio 113</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 diesisiete problemas del Ejercicio 113:</FONT></div> <div> <B>H</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >allar, por divisiones sucesivas, el m.c.d. de:</FONT></div> <div> <IMG SRC="8090f91b0.gif" border=0 width="249" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#1" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="80910c1b0.gif" border=0 width="268" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#2_1" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="80923b1b0.gif" border=0 width="315" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#3" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="8093341b0.gif" border=0 width="308" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#4" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="80948b1b0.gif" border=0 width="395" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#5" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="8095fb1b0.gif" border=0 width="507" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#6" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="8096e71b0.gif" border=0 width="487" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="#7" TITLE="113"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>     <IMG SRC="8097a11b0.gif" border=0 width="417" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/_2a53ZhWMRE" TARGET="_top" TITLE="https://youtu.be/_2a53ZhWMRE"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="8098db1b0.gif" border=0 width="475" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/7WCXd6LP8Bo" TARGET="_top" TITLE="https://youtu.be/7WCXd6LP8Bo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="8099fd1b0.gif" border=0 width="509" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/bNcDFsoTggk" TARGET="_top" TITLE="https://youtu.be/bNcDFsoTggk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="809afb1b0.gif" border=0 width="507" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/FR2rsFruRVM" TARGET="_top" TITLE="https://youtu.be/FR2rsFruRVM"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="809bc51b0.gif" border=0 width="453" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/ZZeTogN2cBA" TARGET="_top" TITLE="https://youtu.be/ZZeTogN2cBA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>     <IMG SRC="809cc91b0.gif" border=0 width="457" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/hsYjfWcOfk4" TARGET="_top" TITLE="https://youtu.be/hsYjfWcOfk4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="809dd11b0.gif" border=0 width="465" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/mhjR01CODSA" TARGET="_top" TITLE="https://youtu.be/mhjR01CODSA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <div> <IMG SRC="809e3b1b0.gif" border=0 width="571" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">      <IMG SRC="809f531b0.gif" border=0 width="339" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="80a0511b0.gif" border=0 width="593" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <B>Soluciones de los problemas del Ejercicio 113</B></div> <bR> <div> <B> <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo3FxKelf2Qp5xi0y1SLKMTt" frameborder="0" allowfullscreen></iframe>  </B></div> <div> <B>H</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >allar, por divisiones sucesivas, el m.c.d. de:</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="5d7a486c0.gif" border=0 width="840" height="364" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></div> <div> <IMG SRC="5dc36ddd0.gif" border=0 width="877" height="477" 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="5dc4df150.gif" border=0 width="991" height="533" 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="5d7b3d6d0.gif" border=0 width="829" height="365" ALT="MathType 5.0 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="5dc564500.gif" border=0 width="868" height="592" 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="5d7ccdd00.gif" border=0 width="973" height="720" ALT="MathType 5.0 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="5dc69d910.gif" border=0 width="925" height="657" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 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