document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65543>Question 65543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I dont understand\r<BR>\n" );
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document.write( "\"The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3+i among its roots.  Express f(x) as a product of linear and quadratic polynomials with real coefficients.\"\r<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 #46095 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=46095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3+i among its roots.  Express f(x) as a product of linear and quadratic polynomials with real coefficients.\"\r<BR>\n" );
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document.write( "There are two rules involved:<BR>\n" );
document.write( "1. If a is a root, x-a is a factor<BR>\n" );
document.write( "2. If a+bi is a root, and all coefficients of f(x) are Real, then a-bi is a root.<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "f(x)=(x-4)(x-(3+i))(x-(3-i))<BR>\n" );
document.write( "    =(x-4)((x-3)-i)((x-3)+i)<BR>\n" );
document.write( "    =(x-4)((x-3)^2+1)<BR>\n" );
document.write( "    =(x-4)(x^2-6x+10)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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