document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218142>Question 218142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are the zeros for f(x)=x^4-x^3+3x^2-9x-54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164365 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=164365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)= x^4 -x^3 +3x^2 -9x -54<BR>\n" );
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document.write( "zeros  =p/q= (factors  of constant)/ (factors  of leading  coeff)= +/- 54/1<BR>\n" );
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document.write( "or  zeroes  are  factors  of  54,,,+/- 1,54,2,27,3,18,6,9<BR>\n" );
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document.write( "If  we  plot  using  a  graphing  calc,  we  find zero's  at  x=-2,,,x=+3<BR>\n" );
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document.write( "using  synthetic  division  to  confirm,,  and  find  imaginary  zeros<BR>\n" );
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document.write( ".try  x=3<BR>\n" );
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document.write( ".,,,,,3|,,,1,,,-1,,,3,,,-9,,,-54<BR>\n" );
document.write( ".,,,,,,,,,,,,,,3,,,,6,,,,27,,+54<BR>\n" );
document.write( ".,,,,,,,------------------------<BR>\n" );
document.write( ".,,,,,,,,,,1,,,2,,,,9,,,18,,,,0,,,ok,,,,now  try x=-2<BR>\n" );
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document.write( ",,,,,,-2|,,1,,,2,,,,9,,,18<BR>\n" );
document.write( ".,,,,,,,,,,,,,,-2,,,0,,,-18<BR>\n" );
document.write( ",,,,,,,,---------------------<BR>\n" );
document.write( ",,,,,,,,,,,1,,,0,,,,9,,,,,0,,,,,,,,ok<BR>\n" );
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document.write( "Remainder  is  ,,1x^2 +0x +9<BR>\n" );
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document.write( ".This  factors  to  (x+3i)(x-3i),,,,,imaginary  zeros,,,(use  quadratic  formula  if you  don't  remember)<BR>\n" );
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document.write( "Set  of  zeros  is,,,,x=3,,,x=-2,,,x=+3i,,,,x=-3i<BR>\n" );
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document.write( "this  can  be  confirmed  by  multiplying  above  to  get  original<BR>\n" );
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document.write( "check ,,,,(x^2 +9) (x+2)(x-3) = (x^3 +2x^2 +9x +18)(x-3) = x^4 -x^3 +3x^2 =9x -54,,,,,ok<BR>\n" );
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