document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183921>Question 183921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please show me how to factor a polynomial completely thank you\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   -36a2b+21ab2-3b3\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137985 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=137985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor completely: Note: You can indicate exponents by use of the caret symbol (^).  Example - a-squared would look like a^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36a%5E2b%2B21ab%5E2-3b%5E3 ALIGN=MIDDLE  ALT=\"-36a%5E2b%2B21ab%5E2-3b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > First factor out those factors that are common to each term, in this case, I would factor out -3b thus:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3b%2812a%5E2-7ab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"-3b%2812a%5E2-7ab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the change of sign on each factor when you factor the -3.<BR>\n" );
document.write( "Now to factor the trinomial in parentheses, first look at the leading term, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%5E2 ALIGN=MIDDLE  ALT=\"12a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and note that this can be factored as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%5E2+=+1%2A12%2Aa%2Aa ALIGN=MIDDLE  ALT=\"12a%5E2+=+1%2A12%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A-12%2Aa%2Aa ALIGN=MIDDLE  ALT=\"-1%2A-12%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%5E2+=+2%2A6%2Aa%2Aa ALIGN=MIDDLE  ALT=\"12a%5E2+=+2%2A6%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A-6%2Aa%2Aa ALIGN=MIDDLE  ALT=\"-2%2A-6%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%5E2+=+3%2A4%2Aa%2Aa ALIGN=MIDDLE  ALT=\"12a%5E2+=+3%2A4%2Aa%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-3%2A-4%2Aa%2Aa%29 ALIGN=MIDDLE  ALT=\"highlight%28-3%2A-4%2Aa%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now notice the middle term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7ab ALIGN=MIDDLE  ALT=\"-7ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > The only way to factor this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7ab+=+-7%2Aa%2Ab ALIGN=MIDDLE  ALT=\"-7ab+=+-7%2Aa%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you can get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-3%2B%28-4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28-3%2B%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can only be factored as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b%2Ab%29 ALIGN=MIDDLE  ALT=\"highlight%28b%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So putting it all together, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36a%5E2b%2B21ab%5E2-3b%5E3+=+highlight%28-3b%283a-b%29%284a-b%29%29 ALIGN=MIDDLE  ALT=\"-36a%5E2b%2B21ab%5E2-3b%5E3+=+highlight%28-3b%283a-b%29%284a-b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );