document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010032>Question 1010032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> n=3<BR>\n" );
document.write( "2 and 2i are zeros<BR>\n" );
document.write( "f(-1)=-15<BR>\n" );
document.write( "What does f(x) = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625500 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=625500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n=3 ALIGN=MIDDLE  ALT=\"+n=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > are zeros<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=+-2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=+-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero too, complex zeros always come in pairs<BR>\n" );
document.write( "so, we use zero product theorem to find the polynomial\r<BR>\n" );
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document.write( "given also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-15 ALIGN=MIDDLE  ALT=\"f%28-1%29=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but since all three roots are given, this will not be used\r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+%28x-x%5B1%5D%29+%28x-x%5B2%5D%29+%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"+f%28x%29+=+%28x-x%5B1%5D%29+%28x-x%5B2%5D%29+%28x-x%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x-2i%29+%28x-%28-2i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x-2i%29+%28x-%28-2i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x-2i%29+%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x-2i%29+%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x%5E2-%282i%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x%5E2-%282i%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x%5E2-4%28i%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x%5E2-4%28i%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x%5E2-4%28-1%29%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x%5E2-4%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29+%28x%5E2%2B4%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29+%28x%5E2%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E3%2B4x-2x%5E2-8 ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E3%2B4x-2x%5E2-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3-2x%5E2%2B4x-8 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3-2x%5E2%2B4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> your answer\r<BR>\n" );
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document.write( "now, we can check if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-15 ALIGN=MIDDLE  ALT=\"f%28-1%29=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+%28-1%29%5E3-2%28-1%29%5E2%2B4%28-1%29-8 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+%28-1%29%5E3-2%28-1%29%5E2%2B4%28-1%29-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+-1-2%281%29-4-8 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+-1-2%281%29-4-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+-1-2-4-8 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+-1-2-4-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+-15 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );