document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281596>Question 281596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor as completely as possible.<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-4x ALIGN=MIDDLE  ALT=\"x%5E3-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-x%2B8y-8 ALIGN=MIDDLE  ALT=\"xy-x%2B8y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2-90x ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2-90x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hello! You dont have to do all three of these (unless you want too; go ahead and knock yourself out ;) ) What I wanted to know was if someone could please explain to me how I would factor these as completely as possible?<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204571 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=204571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll knock myself out ;)\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-4x ALIGN=MIDDLE  ALT=\"x%5E3-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-x%2B8y-8 ALIGN=MIDDLE  ALT=\"xy-x%2B8y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2-90x ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2-90x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) We first want to look for any greatest common factors, notice there is an x in each term which is our greatest common factor!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+4x+=+x%28x%5E2+-+4%29 ALIGN=MIDDLE  ALT=\"x%5E3+-+4x+=+x%28x%5E2+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how an x comes out of both terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+-+4%29+=+x%28x%2B2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2+-+4%29+=+x%28x%2B2%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is binomial factoring, we can do this because there is a minus sign in between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. also, both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be square rooted perfectly.\r<BR>\n" );
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document.write( "So the final answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%28x%2B2%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x%28x%2B2%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) This example is a super use of greatest common factoring, sometimes noted as gcd:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-x%2B8y-8 ALIGN=MIDDLE  ALT=\"xy-x%2B8y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > group the first two together and the last two:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy+-+x%29+%2B+%288y+-+8%29 ALIGN=MIDDLE  ALT=\"%28xy+-+x%29+%2B+%288y+-+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then factor by greatest common factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28y-1%29+%2B+8%28y+-+1%29 ALIGN=MIDDLE  ALT=\"x%28y-1%29+%2B+8%28y+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that there are two y-1, we can factor that out too:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29+%28x+%2B+8%29 ALIGN=MIDDLE  ALT=\"%28y-1%29+%28x+%2B+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the easiest way to see this step is to take out the y-1 and whatever is left over is your second term.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28y-1%29+%28x+%2B+8%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28y-1%29+%28x+%2B+8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is your final answer\r<BR>\n" );
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document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2-90x ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2-90x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Once again start off with greatest common factoring, there is an x is each of those:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+%2B+x+-+90%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2+%2B+x+-+90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we want to find two things that multiply to be negative 90 and add up to be positive 1. One number is going to have to be a negative because that is the only way to multiply two numbers to get -90. The answer for this one is -9 and +10 which reduces to our final factoring:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+%28x+%2B+10%29+%28x+-+9%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x+%28x+%2B+10%29+%28x+-+9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > final answer<BR>\n" );
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