document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46540>Question 46540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factoring polynomials of the form ax^2+bx+c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4x^2-27x+18<BR>\n" );
document.write( "I can figure the factors of 4 and the factors of 18<BR>\n" );
document.write( "but I'm lost with the trial factors and middle term<BR>\n" );
document.write( "not really sure as to its purpose </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30830 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=30830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, there'e a bit of trial-and-error processing that occurs when you try to facto a trinomial whose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient is greater than 1.\r<BR>\n" );
document.write( "\n" );
document.write( "Here's the way I go about it:\r<BR>\n" );
document.write( "\n" );
document.write( "I know that the factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2 ALIGN=MIDDLE  ALT=\"4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x++%29%28x++%29 ALIGN=MIDDLE  ALT=\"%284x++%29%28x++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x++%29%282x++%29 ALIGN=MIDDLE  ALT=\"%282x++%29%282x++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The factors of 18 are: (1)(18) or (2)(9) or (3)(6)\r<BR>\n" );
document.write( "\n" );
document.write( "I also notice that the middle term of the trinomial is negative and the last term is positive.  This tells me that the contants part of the factors are both negative numbers.<BR>\n" );
document.write( " Why? Because a negative times a negative is a positive (last term is positive) and a negative plus a negative is a negative (middle term is negative)\r<BR>\n" );
document.write( "\n" );
document.write( "Try the first pair of factors with the x's\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+1%29%28x+-+18%29+=+4x%5E2+-72x+-+x+%2B+18 ALIGN=MIDDLE  ALT=\"%284x+-+1%29%28x+-+18%29+=+4x%5E2+-72x+-+x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+73x+%2B+18 ALIGN=MIDDLE  ALT=\"4x%5E2+-+73x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >No go! The middle term is wrong.\r<BR>\n" );
document.write( "\n" );
document.write( "Try:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+2%29%28x+-+9%29+=+4x%5E2+-36x+-2x+%2B+18 ALIGN=MIDDLE  ALT=\"%284x+-+2%29%28x+-+9%29+=+4x%5E2+-36x+-2x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+38x+%2B+18 ALIGN=MIDDLE  ALT=\"4x%5E2+-+38x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > No go! The middle term is wrong.\r<BR>\n" );
document.write( "\n" );
document.write( "Try:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+-+3%29%28x+-+6%29+=+4x%5E2+-+24x+-+3x+%2B+18 ALIGN=MIDDLE  ALT=\"%284x+-+3%29%28x+-+6%29+=+4x%5E2+-+24x+-+3x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+27x+%2B+18 ALIGN=MIDDLE  ALT=\"4x%5E2+-+27x+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Bingo!\r<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );