document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920749>Question 920749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12x^2-29x+15=0 ( Factor)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558554 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=558554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Try thinking of the quadratic trinomial this way.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax%2Bb%29%28cx%2Bd%29=12x%5E2-29%2B15 ALIGN=MIDDLE  ALT=\"%28ax%2Bb%29%28cx%2Bd%29=12x%5E2-29%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ac%2Ax%5E2%2Bbcx%2Badx%2Bbd ALIGN=MIDDLE  ALT=\"ac%2Ax%5E2%2Bbcx%2Badx%2Bbd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ac%2Ax%5E2%2B%28bc%2Bad%29x%2Bbd ALIGN=MIDDLE  ALT=\"ac%2Ax%5E2%2B%28bc%2Bad%29x%2Bbd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Compare the coefficients to form the equations:<BR>\n" );
document.write( "ac=12, -29=bc+ad, bd=15<BR>\n" );
document.write( "Three equations but FOUR unknown variables.  You at least expect a,b,c,d to all be integers, and be nonzero.\r<BR>\n" );
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document.write( "You can make logical trials and test them.<BR>\n" );
document.write( "a and c not relying on order nor sign, would be one of 1 & 12; 2 &6, 3 & 4. <BR>\n" );
document.write( "b and d similarly would be one of 1 & 15, or 3 & 5.\r<BR>\n" );
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document.write( "Do what you are able with those facts.\r<BR>\n" );
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document.write( "A more advanced way to factorize is to use the discriminant:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-29%29%5E2-4%2A12%2A15=121 ALIGN=MIDDLE  ALT=\"%28-29%29%5E2-4%2A12%2A15=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=121=highlight%2811%5E2%29 ALIGN=MIDDLE  ALT=\"121=highlight%2811%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "This means that the ROOTS for x are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829-11%29%2F24 ALIGN=MIDDLE  ALT=\"%2829-11%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829%2B11%29%2F24 ALIGN=MIDDLE  ALT=\"%2829%2B11%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F24=3%2F4 ALIGN=MIDDLE  ALT=\"18%2F24=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F24=8%2F3 ALIGN=MIDDLE  ALT=\"40%2F24=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "This then means you can choose a form for your quadratic expression,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%28x-3%2F4%29%28x-8%2F3%29%29 ALIGN=MIDDLE  ALT=\"highlight%2812%28x-3%2F4%29%28x-8%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which you could refactor if you want to. </SPAN>\n" );
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