document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=12560>Question 12560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to learn about the quadratic equations. I know how to turn (3x-4)(2x+1)=0, but I don't know how to turn 6x^2 -5x -4=0 into (3x-4)(2x+1)=0.<BR>\n" );
document.write( "-Sarah </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6373 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=6373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, going from:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29%282x%2B1%29 ALIGN=MIDDLE  ALT=\"%283x-4%29%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-5x-5 ALIGN=MIDDLE  ALT=\"6x%5E2-5x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a whole lot easier than going the other way.\r<BR>\n" );
document.write( "\n" );
document.write( "Here are some things you might try on factoring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+-+5x+-+4 ALIGN=MIDDLE  ALT=\"6x%5E2+-+5x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for example:\r<BR>\n" );
document.write( "\n" );
document.write( "1)  Look at the first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and ask...how can I factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "There aren't that many ways to factor it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%29%28x%29+=+6x%5E2 ALIGN=MIDDLE  ALT=\"%286x%29%28x%29+=+6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%283x%29+=+6x%5E2 ALIGN=MIDDLE  ALT=\"%282x%29%283x%29+=+6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6x%29%28-x%29+=+6x%5E2 ALIGN=MIDDLE  ALT=\"%28-6x%29%28-x%29+=+6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2x%29%28-3x%29+=+6x%5E2 ALIGN=MIDDLE  ALT=\"%28-2x%29%28-3x%29+=+6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Now look at the last term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and go through the same process.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%284%29+=+-4%29 ALIGN=MIDDLE  ALT=\"%28-1%29%284%29+=+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%28-4%29+=+-4 ALIGN=MIDDLE  ALT=\"%281%29%28-4%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%28-2%29+=+-4 ALIGN=MIDDLE  ALT=\"%282%29%28-2%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%282%29+=+-4 ALIGN=MIDDLE  ALT=\"%28-2%29%282%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is really the same as the one above.\r<BR>\n" );
document.write( "\n" );
document.write( "Now, keeping in mind that you want -5x as the middle term, you can try a pair of factors from the first group with a pair of factors from the second group.\r<BR>\n" );
document.write( "\n" );
document.write( "For example: Try (6x - 1)(x + 4) and you see, almost right away that, while you get the first and last terms of your quadratic, you do not get -5x as the middle term. The same with (6x + 1)(x - 4) and (6x + 4)(x - 1).<BR>\n" );
document.write( "Now try (3x + 1)(2x - 4) again, you don't get the middle term of -5x, so try (3x - 4)(2x + 1) Now you get a middle term of -5x from 3x - 8x = -5x.\r<BR>\n" );
document.write( "\n" );
document.write( "So, these are the required factors. \r<BR>\n" );
document.write( "\n" );
document.write( "It's a little harder when, as in this case, the coefficient of the x^2 term is greater than 1. Indeed, in some cases, you may not be able to factor the quadratic at all. But, you can always solve a quadratic equation by using the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I hope this is some help.  I have one math book on Intermediate Algebra that devotes some 36 pages to the topic of factoring polynomials.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );