document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042147>Question 1042147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an&#8203; nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing&#8203; utility, use it to graph the function and verify the real zeros and the given function value.\r<BR>\n" );
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document.write( "n=3<BR>\n" );
document.write( "-4 and 1+2i are zeros<BR>\n" );
document.write( "f(2)=30\r<BR>\n" );
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document.write( "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 #657118 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=657118\">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=f%28x%29=a%28x%2B4%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%2B4%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a is unknown factor, determinable later using x=2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x%2B4%29%28x-1-2i%29%28x-1%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%2B4%29%28x-1-2i%29%28x-1%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x%2B4%29%28%28x-1%29-2i%29%28%28x-1%29%2B2i%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%2B4%29%28%28x-1%29-2i%29%28%28x-1%29%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B4%29%28x%5E2-2x%2B1-4%28-1%29%29 ALIGN=MIDDLE  ALT=\"a%28x%2B4%29%28x%5E2-2x%2B1-4%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=a%28x%2B4%29%28x%5E2-2x%2B5%29%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=a%28x%2B4%29%28x%5E2-2x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FINDING FACTOR a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=30 ALIGN=MIDDLE  ALT=\"f%282%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > as given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282%2B4%29%282%5E2-2%2A2%2B5%29=30 ALIGN=MIDDLE  ALT=\"a%282%2B4%29%282%5E2-2%2A2%2B5%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A6%2A5=30 ALIGN=MIDDLE  ALT=\"a%2A6%2A5=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "THE FUNCTION f<BR>\n" );
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document.write( "Do the multiplication to put into general polynomial form. </SPAN>\n" );
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