document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943336>Question 943336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I factor completely 9y^2-6y+6? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575128 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=575128\">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=3%2A3y%5E2-2%2A3y%2B2%2A3 ALIGN=MIDDLE  ALT=\"3%2A3y%5E2-2%2A3y%2B2%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%283y%5E2-2y%2B2%29 ALIGN=MIDDLE  ALT=\"3%283y%5E2-2y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find sensible integer combinations to try.<BR>\n" );
document.write( "(3y____1)(y_____2)<BR>\n" );
document.write( "Gives a 1y and a 6y.  This will not give -2y.\r<BR>\n" );
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document.write( "(3y_____2)(y______1)<BR>\n" );
document.write( "Gives 2y and 3y.  This will not give -2y.\r<BR>\n" );
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document.write( "Next thing to try is roots for factoring the quadratic factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%286%2B-+sqrt%2836-4%2A3%2A2%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"y=%286%2B-+sqrt%2836-4%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=y=%286%2B-+sqrt%2836-24%29%29%2F6 ALIGN=MIDDLE  ALT=\"y=%286%2B-+sqrt%2836-24%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the discriminant is 36-24=12, which will still give an irrational discriminant.\r<BR>\n" );
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document.write( "The original expression is not factorable the way you want it, but can only go as far as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%283y%5E2-2y%2B2%29%29 ALIGN=MIDDLE  ALT=\"highlight%283%283y%5E2-2y%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The factoring can go further, but you would need to accept irrational roots. </SPAN>\n" );
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