document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172003>Question 1172003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.<BR>\n" );
document.write( "−2, 0, 4 + i;    degree 4<BR>\n" );
document.write( "f(x) = <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796911 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=796911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if 4+i is a root, then 4-i is a root, since complex roots are conjugate.<BR>\n" );
document.write( "two of the factors are (x+2) and x<BR>\n" );
document.write( "The other two are from (x-4-i) and (x-4+i)<BR>\n" );
document.write( "If we multiply those factors together, we get <BR>\n" );
document.write( "x^2-4x+ix-4x+16+4i-ix+4i-i^2=x^2-8x+17\r<BR>\n" );
document.write( "\n" );
document.write( "The factors are x, (x+2), and x^2-8x+17. <BR>\n" );
document.write( "f(x) is their product, or x(x+2)(x^2-8x+17) </SPAN>\n" );
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