document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281528>Question 281528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are ways for factoring in an organized way? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204526 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathematicians><B>Mathematicians(84)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathematicians><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=Mathematicians><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=204526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting from easiest to most complicated:\r<BR>\n" );
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document.write( "Greatest common factoring:<BR>\n" );
document.write( "Take out the greatest common factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+5 ALIGN=MIDDLE  ALT=\"5x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since 5 is in both:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"+5%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Trinomial factoring (easy):<BR>\n" );
document.write( "This example will have nothing near the x^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You need to find two things that add up to 3 and multiply to be 2.<BR>\n" );
document.write( "In this case, 1 and 2 are your answers because 1 + 2 = 3 and 1 * 2 = 2\r<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+2+=+%28x%2B2%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+2+=+%28x%2B2%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor by grouping:<BR>\n" );
document.write( "This will not work all the time.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+x%5E2+%2B+x+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+x%5E2+%2B+x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Group the first two terms and the last two terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+x%5E2%29+%2B+%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+x%5E2%29+%2B+%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can use greatest common factoring, x^2 is the same in the first two terms and 1 is the same in the next two.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x%2B1%29+%2B+1%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x%5E2%28x%2B1%29+%2B+1%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this step, you can tell if grouping will work, you will see that we have two (x+1), from this step, you can factor out an (x+1) from each term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B1%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B1%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > many people see this step as taking only one of the (x+1) terms and taking the x^2, and the +1 and put it together.\r<BR>\n" );
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document.write( "Trinomial factoring (hard):<BR>\n" );
document.write( "This example will have something near the x^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+%2B+6x+%2B+1 ALIGN=MIDDLE  ALT=\"9x%5E2+%2B+6x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The method to do this one is to multiply the first and last number together:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+%2A+1+=+9 ALIGN=MIDDLE  ALT=\"+9+%2A+1+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you want to do something similar to the first one, two things that multiply to be 9 and add up to be 6. The answer is 3 and 3, so we divide the middle up like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+%2B+3x+%2B+3x+%2B+1 ALIGN=MIDDLE  ALT=\"9x%5E2+%2B+3x+%2B+3x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If all went right, you can factor by grouping:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%289x%5E2+%2B+3x%29+%2B+%283x+%2B+1%29+=+3x%283x+%2B++1%29+%2B+1%283x+%2B+1%29+=+%283x+%2B+1%29%283x+%2B+1%29+=+%283x+%2B+1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Those should be all the factoring methods you will need to know, the other one is much tougher but is very tricky and is taught at higher levels.\r<BR>\n" );
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