document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=334835>Question 334835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the roots of the following polynomial in the complex number system. <BR>\n" );
document.write( "f(x)=x^3-8x^2+36x-80<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 #239911 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=239911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graphing the function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only real root.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C6%2C-4%2C4%2Cx%5E3-8x%5E2%2B36x-80%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C6%2C-4%2C4%2Cx%5E3-8x%5E2%2B36x-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use polynomial long division to find the remaining quadratic equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-8x%5E2%2B36x-80%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%5E3-8x%5E2%2B36x-80%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First term : <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x-4%29=x%5E3-4x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%28x-4%29=x%5E3-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract this product from the original polynomial to get the remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-8x%5E2%2B36x-80%29-%28x%5E3-4x%5E2%29=-4x%5E2%2B36x-80 ALIGN=MIDDLE  ALT=\"%28x%5E3-8x%5E2%2B36x-80%29-%28x%5E3-4x%5E2%29=-4x%5E2%2B36x-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Second term : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x ALIGN=MIDDLE  ALT=\"-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%28x-4%29=+-4x%5E2%2B16x ALIGN=MIDDLE  ALT=\"-4x%28x-4%29=+-4x%5E2%2B16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract this product from the remainder to get the new remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+-4x%5E2%2B36x-80%29-%28-4x%5E2%2B16x%29=20x-80 ALIGN=MIDDLE  ALT=\"%28+-4x%5E2%2B36x-80%29-%28-4x%5E2%2B16x%29=20x-80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Final term : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%28x-4%29=20x-80 ALIGN=MIDDLE  ALT=\"20%28x-4%29=20x-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract this product from the remainder to get the new remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+20x-80%29-%2820x-80%29=0 ALIGN=MIDDLE  ALT=\"%28+20x-80%29-%2820x-80%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Gather the terms,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-8x%5E2%2B36x-80%29%2F%28x-4%29=%28x%5E2-4x%2B20%29 ALIGN=MIDDLE  ALT=\"%28x%5E3-8x%5E2%2B36x-80%29%2F%28x-4%29=%28x%5E2-4x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete the square to get the remaining roots,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B20=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B4%2B16=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=-16 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=0+%2B-+4i ALIGN=MIDDLE  ALT=\"x-2=0+%2B-+4i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2+%2B-+4i ALIGN=MIDDLE  ALT=\"x=2+%2B-+4i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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