document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=370439>Question 370439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do u factor this trinomial 10a^2-9a+2 ? <BR>\n" );
document.write( "Ex. 3x^2+10x+8 <BR>\n" );
document.write( "    (4)(2)=8 <BR>\n" );
document.write( "    (3x+4)(x+2)<BR>\n" );
document.write( "    (3x)(2)=6x <BR>\n" );
document.write( "    (4)(x)=4x <BR>\n" );
document.write( "    6x+4x=10x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #264210 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=264210\">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=10a%5E2-9a%2B2 ALIGN=MIDDLE  ALT=\"10a%5E2-9a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With the 10 and 2 being positive and with the -9 in the middle, we can tell that the factors, if any, will both have minus signs, After all, we want products that are positive but a sum that is negative. So our factors will be of the form:<BR>\n" );
document.write( "(  -  )(  -  )<BR>\n" );
document.write( "(If you don't see this, then it will just take you longer to factor because you will be trying<BR>\n" );
document.write( "(  +  )(  +  )<BR>\n" );
document.write( "(  -  )(  +  )<BR>\n" );
document.write( "(  +  )(  -  )<BR>\n" );
document.write( "with no hope of any of these working.)<br><BR>\n" );
document.write( "For the 10 in front we know that the factors are either 5 and 2 or 10 and 1. For the two in the back the only factors are 1 and 2. So the possibilities are:<BR>\n" );
document.write( "(5a - 2)(2a - 1)<BR>\n" );
document.write( "(5a - 1)(2a - 2)<BR>\n" );
document.write( "(10a - 2)(a - 1)<BR>\n" );
document.write( "(10a - 1)(a - 2)<BR>\n" );
document.write( "The middle two:<BR>\n" );
document.write( "(5a - 1)(2a - 2)<BR>\n" );
document.write( "(10a - 2)(a - 1)<BR>\n" );
document.write( "can't work because one of the factors has a common factor. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E2-9a%2B2 ALIGN=MIDDLE  ALT=\"10a%5E2-9a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not have a common factor, we can't magically get one later. So we are now left with just:<BR>\n" );
document.write( "(5a - 2)(2a - 1)<BR>\n" );
document.write( "(10a - 1)(a - 2)<BR>\n" );
document.write( "If you multiply these out, you will find that the first one works. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E2-9x%2B2+=+%285a-1%29%282a-1%29 ALIGN=MIDDLE  ALT=\"10a%5E2-9x%2B2+=+%285a-1%29%282a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );