document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745584>Question 745584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial with real coefficients of degree 3 and roots (3,2i,-2i) and that has factors :, (x-3), (x-2i) and (x+2i) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453914 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-3), (x-2i) and (x+2i) tells us...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=a%28x-3%29%28x-2i%29%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"p=a%28x-3%29%28x-2i%29%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "for some constant a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2i%29%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"%28x-2i%29%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "...is a difference of squares - with a twist:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2i%29%28x%2B2i%29=x%5E2%2B4 ALIGN=MIDDLE  ALT=\"%28x-2i%29%28x%2B2i%29=x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so we now use distribution...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=a%28x-3%29%28x%5E2%2B4%29=a%28x%28x%5E2%2B4%29-3%28x%5E2%2B4%29%29 ALIGN=MIDDLE  ALT=\"p=a%28x-3%29%28x%5E2%2B4%29=a%28x%28x%5E2%2B4%29-3%28x%5E2%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=a%28x%5E3%2B4x-3x%5E2-12%29%29 ALIGN=MIDDLE  ALT=\"p=a%28x%5E3%2B4x-3x%5E2-12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=a%28x%5E3-3x%5E2%2B4x-12%29%29 ALIGN=MIDDLE  ALT=\"p=a%28x%5E3-3x%5E2%2B4x-12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "with the principal polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-3x%5E2%2B4x-12 ALIGN=MIDDLE  ALT=\"x%5E3-3x%5E2%2B4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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