document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=681921>Question 681921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial f(x)of degree 3 with real coefficients and the following zeros.\r<BR>\n" );
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document.write( "4,2+i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423008 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=423008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given zeros<BR>\n" );
document.write( "4 and 2+i<BR>\n" );
document.write( "...<BR>\n" );
document.write( "unstated but known<BR>\n" );
document.write( "2-i as it is the conjugate pair<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x=4, so x-4=0<BR>\n" );
document.write( "x=2+/-i, so x-2= +/- i; therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-2%29%5E2+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-2%29%5E2+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=-1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Taking (x-4) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B2%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and multiplying them<BR>\n" );
document.write( "(x-4)(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B3 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+4x%5E2+%2B+3x+-+4x%5E2+%2B+16x+-+12 ALIGN=MIDDLE  ALT=\"x%5E3+-+4x%5E2+%2B+3x+-+4x%5E2+%2B+16x+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E3+-+8x%5E2+%2B+19x+-+12%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E3+-+8x%5E2+%2B+19x+-+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<BR>\n" );
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document.write( " </SPAN>\n" );
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