document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891074>Question 891074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^3-13x+12=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539481 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can you factorize?  Try checking possible rational roots.  Choose from  plus or minus 1,2,3,4,6, maybe 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using synthetic division to check rational roots:<BR>\n" );
document.write( "<b>1 is a root</b>.  The binomial factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This means, the cubic expression in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%5E2-12x-12%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%5E2-12x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now check the quadratic factor:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144-4%2A%28-12%29=144%2B48=192 ALIGN=MIDDLE  ALT=\"144-4%2A%28-12%29=144%2B48=192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192=4%2A48=4%2A12%2A4=4%2A4%2A4%2A3 ALIGN=MIDDLE  ALT=\"192=4%2A48=4%2A12%2A4=4%2A4%2A4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812%2B-+sqrt%284%2A4%2A4%2A3%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2812%2B-+sqrt%284%2A4%2A4%2A3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812%2B-+sqrt%282%5E6%2A3%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2812%2B-+sqrt%282%5E6%2A3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812%2B-+8sqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2812%2B-+8sqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%2B-+4sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%2B-+4sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----the other two roots.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );