document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971583>Question 971583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 3i is a zero of f(x)= x^4-2x^3+6x^2-18x-27, find all the zeros and write the answer in factored form. Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594016 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=594016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)= x^4-2x^3+6x^2-18x-27\r<BR>\n" );
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document.write( "(x+3i)  (x-3i) are factors, since they are conjugate.\r<BR>\n" );
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document.write( "These multiply to x^2-9i^2=x^2+9\r<BR>\n" );
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document.write( "The other factor must contain a -3, since the constant is -27\r<BR>\n" );
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document.write( "Divide that into the original polynomial, and we get x^2-2x-3= (x-3) (x+1)\r<BR>\n" );
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document.write( "The zeros are +/- 3i , 3, -1 .  The latter two produce 0 in the polynomial.\r<BR>\n" );
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document.write( "The factored form is (x+3i)(x-3i)(x-3)(x+1)\r<BR>\n" );
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