document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989210>Question 989210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor the polynomial.<BR>\n" );
document.write( "x^3+3x^2+2x+6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609585 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=609585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "If this polynomial has rational factors they must come from the set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left\{\pm{1},\,\pm{2},\,\pm{3},\,\pm{6}\right\}\">\r<BR>\n" );
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document.write( "Use synthetic division to determine the first factor.  If you need a refresher on synthetic division, see <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/synthdiv.htm\">Purple Math Synthetic  Division</a>  Note that this section of the Purple Math website consists of four pages; read them all.\r<BR>\n" );
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document.write( "One of the divisors will work and I'll leave it up to you to find that divisor.  But the quotient when you do find the correct one will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\ +\ 2\">.  This polynomial does not factor over the real numbers, so if your domain is the Reals, you are done.  However, the quadratic binomial does factor over the complex numbers, thus:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ i\sqrt{2})(x\ -\ i\sqrt{2})\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\"> is the imaginary number defined as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i^2\ =\ -1\">\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" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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