document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127400>Question 127400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to simplify the polynomial and i am really confused. This problem is so different then the examples given in the text...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%28x%5E5%29%5E2 ALIGN=MIDDLE  ALT=\"3x%28x%5E5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%5E3%28x%5E2%29%5E4+ ALIGN=MIDDLE  ALT=\"6x+%5E3%28x%5E2%29%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93443 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=93443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%28x%5E5%29%5E2 ALIGN=MIDDLE  ALT=\"3x%28x%5E5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%5E3%28x%5E2%29%5E4+ ALIGN=MIDDLE  ALT=\"6x+%5E3%28x%5E2%29%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "or<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%28x%5E5%29%5E2%29%2F%286x+%5E3%28x%5E2%29%5E4+%29 ALIGN=MIDDLE  ALT=\"%283x%28x%5E5%29%5E2%29%2F%286x+%5E3%28x%5E2%29%5E4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can think of this in two ways. You multiply the exponent 2 <BR>\n" );
document.write( "times the exponent 5 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10 ALIGN=MIDDLE  ALT=\"x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > times itself to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5+%2Ax%5E5+=+x%5E%285%2B5%29+=+x%5E10 ALIGN=MIDDLE  ALT=\"x%5E5+%2Ax%5E5+=+x%5E%285%2B5%29+=+x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In either case, you substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10 ALIGN=MIDDLE  ALT=\"x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E5%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the numerator and the problem<BR>\n" );
document.write( "then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E2%29%5E4%29 ALIGN=MIDDLE  ALT=\"%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E2%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's work on the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E4 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator. If you multiply the two exponents<BR>\n" );
document.write( "you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E4+=+x%5E8 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E4+=+x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is also what you get if you multiply <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;\" > by itself<BR>\n" );
document.write( "4 times. Substituting this into the denominator makes the problem become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E8%29%29 ALIGN=MIDDLE  ALT=\"%283x%28x%5E10%29%29%2F%286x+%5E3%28x%5E8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Back to the numerator. If you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10 ALIGN=MIDDLE  ALT=\"x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > you add the exponents of<BR>\n" );
document.write( "the x terms and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E11 ALIGN=MIDDLE  ALT=\"3x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the numerator.<BR>\n" );
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document.write( "Then to the denominator. In multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11 ALIGN=MIDDLE  ALT=\"x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <BR>\n" );
document.write( "adding the exponents. Then with the factor 6 the denominator becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E11 ALIGN=MIDDLE  ALT=\"6x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. With<BR>\n" );
document.write( "these reductions of the numerator and the denominator the problem then is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E11%29%2F%286x%5E11%29 ALIGN=MIDDLE  ALT=\"%283x%5E11%29%2F%286x%5E11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Dividing the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11 ALIGN=MIDDLE  ALT=\"x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the numerator by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11 ALIGN=MIDDLE  ALT=\"x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the denominator results in<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11%2Fx%5E11+=+x%5E%2811-11%29+=+x%5E0+=+1 ALIGN=MIDDLE  ALT=\"x%5E11%2Fx%5E11+=+x%5E%2811-11%29+=+x%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "[or you could just view this as canceling the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11 ALIGN=MIDDLE  ALT=\"x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the numerator with the counterpart<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E11 ALIGN=MIDDLE  ALT=\"x%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator.] This reduction leaves you with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F6+=+1%2F2 ALIGN=MIDDLE  ALT=\"3%2F6+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And so, the answer to this problem is that it all simplifies down to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and one way you might solve it.<BR>\n" );
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