document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166923>Question 166923</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!!\r<BR>\n" );
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document.write( "Solving Polynomial Equations<BR>\n" );
document.write( "Solve. Identify all double roots.<BR>\n" );
document.write( "(s-6)^3=27(s-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122994 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=122994\">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=%28s-6%29%5E3=27%28s-8%29 ALIGN=MIDDLE  ALT=\"%28s-6%29%5E3=27%28s-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B108s-216+=27%28s-8%29 ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B108s-216+=27%28s-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s-6%29%5E3 ALIGN=MIDDLE  ALT=\"%28s-6%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B108s-216 ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B108s-216\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Hint: Use Pascal's Triangle to expand\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B108s-216+=+27s+-+216 ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B108s-216+=+27s+-+216\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B108s+=+27s ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B108s+=+27s\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 216 to both sides. Notice that they cancel out and go away.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B108s+-+27s+=+0 ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B108s+-+27s+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 27s from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-18s%5E2%2B+81s+=+0 ALIGN=MIDDLE  ALT=\"s%5E3-18s%5E2%2B+81s+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28s%5E2-18s%2B81%29=0 ALIGN=MIDDLE  ALT=\"s%28s%5E2-18s%2B81%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF \"s\" from the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28s-9%29%28s-9%29=0 ALIGN=MIDDLE  ALT=\"s%28s-9%29%28s-9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2-18s%2B81 ALIGN=MIDDLE  ALT=\"s%5E2-18s%2B81\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s-9%29%28s-9%29 ALIGN=MIDDLE  ALT=\"%28s-9%29%28s-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0 ALIGN=MIDDLE  ALT=\"s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-9=0 ALIGN=MIDDLE  ALT=\"s-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-9=0 ALIGN=MIDDLE  ALT=\"s-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0 ALIGN=MIDDLE  ALT=\"s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Now solve for s in each case\r<BR>\n" );
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document.write( "Since we have a repeating answer, our answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0 ALIGN=MIDDLE  ALT=\"s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0 ALIGN=MIDDLE  ALT=\"s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a double root (ie has a multiplicity of 2) </SPAN>\n" );
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