document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458709>Question 458709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots.\r<BR>\n" );
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document.write( "x^3+2x^2+3x+6=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314694 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Applying the rational root theorem, possible rational roots are -6, -3,-2, -1, 1,2,3,6.<BR>\n" );
document.write( "Using the remainder theorem (or synthetic division), trying out x = -2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E3+%2B+2%28-2%29%5E2+%2B+3%28-2%29+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"%28-2%29%5E3+%2B+2%28-2%29%5E2+%2B+3%28-2%29+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Hence x = -2 is a rational root.  After synthetic division, the quotient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which doesn't even have real roots. </SPAN>\n" );
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