document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980149>Question 980149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor the following polynomial completely into linear factors using real or complex roots. Express how many roots there are.  Also, describe the graph of the function.\r<BR>\n" );
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document.write( "x^5-11x^4+13x^3-143x^2=36x-396 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601363 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^5-11x^4+13x^3-143x^2= 36x-396\r<BR>\n" );
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document.write( "x^4(x-11) + 13x^2(x-11) =36 (x-11)<BR>\n" );
document.write( "(x^4+13x^2-36) (x-11)=0<BR>\n" );
document.write( "x=11, 1 root\r<BR>\n" );
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document.write( "(1/2)(-13 +/- sqrt (169+144)) ;; sqrt 313=17.69<BR>\n" );
document.write( "(1/2) (-13+/-17.69)<BR>\n" );
document.write( "x^2=-30.69<BR>\n" );
document.write( "x=+/- i sqrt(30.69)\r<BR>\n" );
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document.write( "x^2=2.345<BR>\n" );
document.write( "x=+/- 1.531\r<BR>\n" );
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document.write( "There are 3 real roots, 11 and a conjugate pair of irrational roots.<BR>\n" );
document.write( "There are two complex roots.<BR>\n" );
document.write( "The graph goes from minus infinity through the negative irrational root, peaks at y=396 at x=0, and then descends through the positive rational root and then ascends again, crossing the x-axis at x=11 ascending to infinity.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-20%2C20%2C-10000%2C10000%2Cx%5E5-11x%5E4%2B13x%5E3-143x%5E2-36x%2B396%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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