document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378418>Question 378418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to figure out if the denominator of this fraction factors any lower than what it is. The fraction is 3x^3+x^2-27x-9/ 2x^3+9x^2-8x-15. I know that I can't factor by grouping because the groups in this polynomial in the denominator wouldn't have anything in common. I am stuck on this problem and don't know what else to try, please help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268855 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=268855\">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( "First use the Rational Roots Theorem which says that if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \alpha_0x^n\ +\ \alpha_1x^{n-1}\ +\ \cdots\ +\ \alpha_{n-1}x\ +\ \alpha_n\ =\ 0\">\r<BR>\n" );
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document.write( "has a rational root then it must be of the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pm\frac{p}{q}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is an integer factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha_n\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\"> is an integer factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha_0\">\r<BR>\n" );
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document.write( "Using that, the only possible rational factors of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x^3\ +\ 9x^2\ -\ 8x\ -\ 15\">\r<BR>\n" );
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document.write( "are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\,\pm\,1,\,x\,\pm\,3,\,x\,\pm\,5,\,x\,\pm\,15,\,x\,\pm\,\frac{1}{2},\,x\,\pm\,\frac{3}{2},\,x\,\pm\,\frac{5}{2},\,x\,\pm\,\frac{15}{2}\">\r<BR>\n" );
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document.write( "Use synthetic division to test these 16 trial divisors until you either find one that divides the original cubic polynomial evenly, leaving you with the successful trial divisor as one factor and a quotient consisting of a quadratic trinomial as another (and hopefully further factorable) factor, or you exhaust all of the possibilities and thereby determine that your denominator is prime.\r<BR>\n" );
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document.write( "If you need a refresher on Synthetic Division, see:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.purplemath.com/modules/synthdiv.htm\">Purple Math: Synthetic Division</a> (There are 4 pages -- read them all).\r<BR>\n" );
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document.write( "Write back and let me know how you make out.\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<BR>\n" );
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