document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189557>Question 189557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use synthetic division to determine f(i) if f(x)=x^3+2x^2-4\r<BR>\n" );
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document.write( "any help would be appreciated, thank you! \r<BR>\n" );
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document.write( "oh by the way here are the choices to choose from: \r<BR>\n" );
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document.write( "A.-5-2i<BR>\n" );
document.write( "B.-5+2i<BR>\n" );
document.write( "C.-6+i<BR>\n" );
document.write( "D.-6-i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142235 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=142235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "First set up the synthetic division table\r<BR>\n" );
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document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "Start by bringing down the leading coefficient 1\r<BR>\n" );
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document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply i by 1 and place the product (which is i)  right underneath the second  coefficient (which is 2)\r<BR>\n" );
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document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD ></TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add i and 2 to get i+2. Place the sum right underneath i.\r<BR>\n" );
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document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD ></TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD >i+2</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply i by i+2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2%2B2i=-1%2B2i ALIGN=MIDDLE  ALT=\"i%5E2%2B2i=-1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and place it right underneath the third  coefficient 0\r<BR>\n" );
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document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD >-1+2i</TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD >i+2</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add -1+2i and 0 to get -1+2i. Place the sum right underneath -1+2i.\r<BR>\n" );
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document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD >-1+2i</TD><TD ></TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD >i+2</TD><TD >-1+2i</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply i by -1+2i to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i%2B2i%5E2=-2-i ALIGN=MIDDLE  ALT=\"-i%2B2i%5E2=-2-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and place the product right underneath the fourth  coefficient -4\r<BR>\n" );
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document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD >-1+2i</TD><TD >-2-i</TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD >i+2</TD><TD >-1+2i</TD><TD ></TD></TR>\n" );
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document.write( "    Add -2-i and -4 to get -6-i. Place the sum right underneath -2-i.\r<BR>\n" );
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document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >i</TD><TD >|</TD><TD >1</TD><TD >2</TD><TD >0</TD><TD >-4</TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD >|</TD><TD ></TD><TD >i</TD><TD >-1+2i</TD><TD >-2-i</TD><TD ></TD></TR>\r\n" );
document.write( "<TR><TD ></TD><TD ></TD><TD >1</TD><TD >i+2</TD><TD >-1+2i</TD><TD >-6-i</TD></TR>\n" );
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document.write( "Since the remainder is -6-i, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28i%29=-6-i ALIGN=MIDDLE  ALT=\"f%28i%29=-6-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, if we plug \"i\" in for \"x\" into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B2x%5E2-4 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B2x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6-i ALIGN=MIDDLE  ALT=\"-6-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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