document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288565>Question 288565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ((z^3)-(z^2)-4)/(z+i) i need to work it out then state the remainder.<BR>\n" );
document.write( "It's revision and i cant remember what to do it would be great if i could get some assistance.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209161 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The division process is shown below in detail.\r<BR>\n" );
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document.write( "Original expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E3-z%5E2-4%29%2F%28z%2Bi%29 ALIGN=MIDDLE  ALT=\"%28z%5E3-z%5E2-4%29%2F%28z%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First you divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3 ALIGN=MIDDLE  ALT=\"z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2 ALIGN=MIDDLE  ALT=\"z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2 ALIGN=MIDDLE  ALT=\"z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+%2B+z%5E2i ALIGN=MIDDLE  ALT=\"z%5E3+%2B+z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+%2B+z%5E2i ALIGN=MIDDLE  ALT=\"z%5E3+%2B+z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2+-+z%5E2i ALIGN=MIDDLE  ALT=\"-z%5E2+-+z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2 ALIGN=MIDDLE  ALT=\"-z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z ALIGN=MIDDLE  ALT=\"-z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z ALIGN=MIDDLE  ALT=\"-z\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2+-+zi ALIGN=MIDDLE  ALT=\"-z%5E2+-+zi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2+-+zi ALIGN=MIDDLE  ALT=\"-z%5E2+-+zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2+-+z%5E2i ALIGN=MIDDLE  ALT=\"-z%5E2+-+z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i+%2B+zi ALIGN=MIDDLE  ALT=\"-z%5E2i+%2B+zi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i ALIGN=MIDDLE  ALT=\"-z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-zi ALIGN=MIDDLE  ALT=\"-zi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-zi ALIGN=MIDDLE  ALT=\"-zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i+-+zi%5E2 ALIGN=MIDDLE  ALT=\"-z%5E2i+-+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i+-+zi%5E2 ALIGN=MIDDLE  ALT=\"-z%5E2i+-+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i+%2B+zi ALIGN=MIDDLE  ALT=\"-z%5E2i+%2B+zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi+%2B+zi%5E2 ALIGN=MIDDLE  ALT=\"zi+%2B+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi ALIGN=MIDDLE  ALT=\"zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"zi+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"zi+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi+%2B+zi%5E2 ALIGN=MIDDLE  ALT=\"zi+%2B+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2+-+i%5E2 ALIGN=MIDDLE  ALT=\"zi%5E2+-+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2 ALIGN=MIDDLE  ALT=\"zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"zi%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"zi%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2+-+i%5E2 ALIGN=MIDDLE  ALT=\"zi%5E2+-+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i%5E2+-+i%5E3 ALIGN=MIDDLE  ALT=\"-i%5E2+-+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then you bring down the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i%5E2+-+i%5E3+-+4 ALIGN=MIDDLE  ALT=\"-i%5E2+-+i%5E3+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can substitute in this last expression to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-1%29+-+%28-1%2Ai%29+-+4 ALIGN=MIDDLE  ALT=\"-%28-1%29+-+%28-1%2Ai%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+i+-+4 ALIGN=MIDDLE  ALT=\"1+%2B+i+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+-+3 ALIGN=MIDDLE  ALT=\"i+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That's your remainder.\r<BR>\n" );
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document.write( "Your answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E3-z%5E2-4%29%2F%28z%2Bi%29 ALIGN=MIDDLE  ALT=\"%28z%5E3-z%5E2-4%29%2F%28z%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+-+3 ALIGN=MIDDLE  ALT=\"i+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To prove that this is correct, you need to multiply the answer by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then add the remainder back in to see if you can duplicate the original expression.\r<BR>\n" );
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document.write( "You do that in the following manner.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Bi ALIGN=MIDDLE  ALT=\"z%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "First we multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then we multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2 ALIGN=MIDDLE  ALT=\"z%5E2+-+z+-+zi+%2B+i+%2B+i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then we add:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > together to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2+%2B+z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+z%5E2i+%2B+zi+%2B+zi%5E2+%2B+z%5E2i+-+zi+-+zi%5E2+%2B+i%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then we combine like terms to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3\"   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=z%5E2i ALIGN=MIDDLE  ALT=\"z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-z%5E2i ALIGN=MIDDLE  ALT=\"-z%5E2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > canceled out.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi ALIGN=MIDDLE  ALT=\"zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-zi ALIGN=MIDDLE  ALT=\"-zi\"   DISABLED_style= \"max-width:90%; height:auto;\" > canceled out.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zi%5E2 ALIGN=MIDDLE  ALT=\"zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-zi%5E2 ALIGN=MIDDLE  ALT=\"-zi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > canceled out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can substitute in this expression to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+%2B+i%5E2+%2B+i%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+1+-+i ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+1+-+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You now need to add the remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+-+3 ALIGN=MIDDLE  ALT=\"i+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > back in.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+1+-+i ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+1+-+i\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+-+3 ALIGN=MIDDLE  ALT=\"i+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+1+-+i+%2B+i+-+3 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+1+-+i+%2B+i+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Combine like results to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+-+z%5E2+-+4 ALIGN=MIDDLE  ALT=\"z%5E3+-+z%5E2+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i ALIGN=MIDDLE  ALT=\"-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > canceled out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since this is the same as the original expression you started with, your division is confirmed as being successfully concluded.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );