document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8427>Question 8427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem on my homework says: Find all factors of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B14x-12+ ALIGN=MIDDLE  ALT=\"6x%5E2%2B14x-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " Help please? Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4649 by </B><A HREF=/tutors/aboutme.mpl?userid=drglass><B>drglass(89)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drglass><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=4649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There a several ways to solve this. The easiest is to use the quadratic equation, however I suspect, given the results I get from the quadratic equation, that you are actually required to factor the problem, so, how do you do this?<br><BR>\n" );
document.write( "First, notice that you result will have to have the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax+%2B+b%29%28cx+%2B+d%29+=+acx%5E2+%2B+%28ad+%2B+bc%29x+%2B+bd ALIGN=MIDDLE  ALT=\"%28ax+%2B+b%29%28cx+%2B+d%29+=+acx%5E2+%2B+%28ad+%2B+bc%29x+%2B+bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The goal is to find the values for a, b, c and d. To do this notice that according to the equation,:<br><BR>\n" );
document.write( "ac = 6,<BR>\n" );
document.write( "ad + bc = 14 and<BR>\n" );
document.write( "bd = -12<br><BR>\n" );
document.write( "There are four possible ways to get ac = 6<br><BR>\n" );
document.write( "a&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ac<BR>\n" );
document.write( "6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<BR>\n" );
document.write( "1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<BR>\n" );
document.write( "3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6<BR>\n" );
document.write( "2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6\r<BR>\n" );
document.write( "\n" );
document.write( "There are twelve ways to get db = -12\r<BR>\n" );
document.write( "\n" );
document.write( "d&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;db<BR>\n" );
document.write( "&nbsp;12&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-1&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "-12&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;&nbsp;1&nbsp;&nbsp;&nbsp;-12&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;-1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;12&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-2&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "-6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;2&nbsp;&nbsp;&nbsp;&nbsp;-6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "-2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-3&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "-4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "&nbsp;3&nbsp;&nbsp;&nbsp;&nbsp;-4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-12<BR>\n" );
document.write( "-3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4&nbsp;&nbsp;&nbsp;&nbsp;-12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With these numbers, there are forty-eight combinations we can used to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ad+%2B+bc ALIGN=MIDDLE  ALT=\"ad+%2B+bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We could list them, or we try to examine the numbers in these tables. As it happens, 6*3 - 1*4 = 14, which is the result we are looking for. This means, the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x+-+4%29%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"%286x+-+4%29%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );