document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086482>Question 1086482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial that has the following characteristics. Show your work.\r<BR>\n" );
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document.write( "  -Its degree is seven.<BR>\n" );
document.write( "  -It has only integer coefficients.<BR>\n" );
document.write( "  -Its zero include -1 as only rational ones.<BR>\n" );
document.write( "  -Its zero include 4i (multiplicity 1) and -2root(2)(multiplicity 1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700727 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=700727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -Its degree is seven.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E7+%2B+bx%5E6+%2B+cx%5E5+%2B+dx%5E4+%2Bex%5E3+%2B+fx%5E2+%2B+gx+%2B+h ALIGN=MIDDLE  ALT=\"ax%5E7+%2B+bx%5E6+%2B+cx%5E5+%2B+dx%5E4+%2Bex%5E3+%2B+fx%5E2+%2B+gx+%2B+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  -It has only integer coefficients.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > are integers\r<BR>\n" );
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document.write( "  -Its zero include <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as only rational ones.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  -Its zero include <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i ALIGN=MIDDLE  ALT=\"4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplicity 1) and -2root(2)(multiplicity 1).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=4i ALIGN=MIDDLE  ALT=\"x%5B2%5D=4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x%5B3%5D=-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "since complex roots and  square root  always come in pairs, we will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=-4i ALIGN=MIDDLE  ALT=\"x%5B4%5D=-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B5%5D=-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x%5B5%5D=-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  too\r<BR>\n" );
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document.write( "since we need seven roots, we use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > three times \r<BR>\n" );
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document.write( "and, using zero product theorem we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B1%29%28x%2B1%29%28x%2B1%29%28x%2B4i%29%28x-4i%29%28x%2B2sqrt%282%29%29%28x%2B2sqrt%282%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when all multiplied, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E7+%2B+3x%5E6+%2B+11x%5E5+%2B+25x%5E4+-+104x%5E3+-+376x%5E2+-+384x+-+128 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E7+%2B+3x%5E6+%2B+11x%5E5+%2B+25x%5E4+-+104x%5E3+-+376x%5E2+-+384x+-+128\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is your polynomial\r<BR>\n" );
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document.write( " </SPAN>\n" );
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