document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181059>Question 181059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am homeschooled with the School of Tomorrow.  I have no teacher, and am struggling with factoring trinomials, particularly coefficients greater than one and complex factoring.  Right now I am trying to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6X%5E2%2B14X%2B4 ALIGN=MIDDLE  ALT=\"6X%5E2%2B14X%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Please help me! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135705 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=135705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+%2B+14x+%2B+4 ALIGN=MIDDLE  ALT=\"6x%5E2+%2B+14x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To locate the roots, set the equation equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+%2B+14x+%2B+4+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2+%2B+14x+%2B+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+7x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+7x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I often try to factor by trying combinations that will<BR>\n" );
document.write( "factor the outside terms and try to get the inside term,<BR>\n" );
document.write( "for instance:<BR>\n" );
document.write( "(3x + ?)(x + ?) I've got the 1st term factored, now for the 3rd<BR>\n" );
document.write( "(3x + 2)(x + 1) Does this work?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+2%29%28x+%2B+1%29+=+3x%5E2+%2B+5x+%2B+2 ALIGN=MIDDLE  ALT=\"%283x+%2B+2%29%28x+%2B+1%29+=+3x%5E2+%2B+5x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > not quite<BR>\n" );
document.write( "How about<BR>\n" );
document.write( "(3x + 1)(x + 2) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+1%29%28x+%2B+2%29+=+3x%5E2+%2B+7x+%2B+2 ALIGN=MIDDLE  ALT=\"%283x+%2B+1%29%28x+%2B+2%29+=+3x%5E2+%2B+7x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that's it<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Some are not this neat, and you have to use the quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use this when the form of the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3 ALIGN=MIDDLE  ALT=\"a+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7 ALIGN=MIDDLE  ALT=\"b+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+2 ALIGN=MIDDLE  ALT=\"c+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Some are not this neat, and you have to use the quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%28+49+-+24+%29%29+%2F+6+ ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49+-+24+%29%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%2825%29+%29+%2F+6+ ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%2825%29+%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+5+%29+%2F+6+ ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+5+%29+%2F+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%287%2F6%29+%2B+%285%2F6%29 ALIGN=MIDDLE  ALT=\"x+=+-%287%2F6%29+%2B+%285%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%281%2F3%29 ALIGN=MIDDLE  ALT=\"x+=+-%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%281%2F3%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+%281%2F3%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%287%2F6%29+-+%285%2F6%29 ALIGN=MIDDLE  ALT=\"x+=+-%287%2F6%29+-+%285%2F6%29\"   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%2F6%29 ALIGN=MIDDLE  ALT=\"x+=+-%2812%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%281%2F3%29%29%28x+%2B+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+%281%2F3%29%29%28x+%2B+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%287%2F3%29x+%2B+%282%2F3%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%287%2F3%29x+%2B+%282%2F3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+7x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+7x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );