document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245871>Question 245871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am learning how to factor equations and am having difficulty with this one.. I can not figure out the GCF to be able to proceed. Not all variables have an X so what do I pull out? \r<BR>\n" );
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document.write( "x^3+8x^2+2x+16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179537 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<b><i>Terminology note:</i></b> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^3\ +\ 8x^2\ +\ 2x\ +\ 16\"> is <b><i>NOT</i></b> an equation.  An equation must have an equal sign in it somewhere, and there is no equal sign to be seen here.  This is a polynomial expression, specifically a 3rd degree polynomial expression.  If this was English class and you claimed that this was a sentence, your teacher would ask \"Where is your verb?\"\r<BR>\n" );
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document.write( "The method illustrated here only works under certain conditions, and in this case those conditions have been contrived by the constructor of the problem.  Keep this in your toolbox, but it is not a magic bullet that is always appropriate to use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^3\ +\ 8x^2\ +\ 2x\ +\ 16\">\r<BR>\n" );
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document.write( "Notice that the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> term is 2 times the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^3\"> term and the constant term is 2 times the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\"> term.\r<BR>\n" );
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document.write( "Rearrange the terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^3\ +\ 2x\ +\ 8x^2\ +\ 16\">\r<BR>\n" );
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document.write( "Group the two pairs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x^3\ +\ 2x\right)\ +\ \left(8x^2\ +\ 16\right)\">\r<BR>\n" );
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document.write( "Factor <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> from the first group and 8 from the second group:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\left(x^2\ +\ 2\right)\ +\ 8\left(x^2\ +\ 2\right)\">\r<BR>\n" );
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document.write( "Now note that the resulting two terms have a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\ +\ 2\"> in common.  Factor it out:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ 8\right)\left(x^2\ +\ 2\right)\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\ +\ 2\"> cannot be factored over the real numbers, if factoring over the real numbers is your assignment, then you are done.  If you are supposed to consider the complex factors, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ 8\right)\left(x\ +\ i\sqrt{2}\right)\left(x\ -\ i\sqrt{2}\right)\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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