document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668777>Question 668777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the complex zeros of the polynomial function. Write f in factored form\r<BR>\n" );
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document.write( "f(x)=x^3-6x^2+13x-20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #415855 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the coefficient of the highest degree, call it Q.  Also consider the coefficient of the lowest degree (the constant) call it P. Find all factors of P and find all factors of Q , and take P/Q for each. Since Q is 1, this won't matter.\r<BR>\n" );
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document.write( "We get that the factors are {1,2,4,5,10,20}, plus or minus of course.<BR>\n" );
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document.write( "We are doing this because we want to find a 0 of the equation. So plug these different values until you get 0. It just so happens x =4.\r<BR>\n" );
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document.write( "Now do synthetic or long division:\r<BR>\n" );
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document.write( "(x^3-6x^2+13x-20)/(x-4) = x^2-2x +5\r<BR>\n" );
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document.write( "To finish this up, do the quadratic formula on x^2-2x+5 to obtain roots:\r<BR>\n" );
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document.write( "1-2i, 1+2i\r<BR>\n" );
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document.write( "Which means in factored form we have (x-4)(x-(1-2i))(x-(1+2i)) </SPAN>\n" );
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