document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785719>Question 785719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is is polynomial function of least degree with real coefficients -4, 2i, and -2i? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477698 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=477698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is not written correctly.  The given values are zeroes instead of coefficients.  Not all of them are real.<P><BR>\n" );
document.write( "To find a polynomial of least degree with the roots -4, 2i and -2i, subtract the zeroes from x to find factors.<P><BR>\n" );
document.write( "x=-4 ---> x+4<P><BR>\n" );
document.write( "x=2i --->x-2i<P><BR>\n" );
document.write( "x=-2i ---> x+2i<P><BR>\n" );
document.write( "Multiply the factors together.  It's wise to multiply the factors involving imaginary numbers together first.<P><BR>\n" );
document.write( "(x-2i)(x+2i) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-4i%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+-4i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B4 ALIGN=MIDDLE  ALT=\"x%5E2+%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<P><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%5E2+%2B+4%29+=+x%5E3+%2B+4x%5E2++%2B4x+%2B+16 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%5E2+%2B+4%29+=+x%5E3+%2B+4x%5E2++%2B4x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "Since some number, a, may have been factored out of each term, multiply the whole thing by a.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%5E3+%2B+4x%5E2++%2B4x+%2B+16%29 ALIGN=MIDDLE  ALT=\"a%28x%5E3+%2B+4x%5E2++%2B4x+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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