document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138685>Question 138685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cost function is given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=%281%2F2%29x%5E3-8x%5E2-80x%2B200 ALIGN=MIDDLE  ALT=\"C%28x%29=%281%2F2%29x%5E3-8x%5E2-80x%2B200\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Find the cost of producing 100 boxes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101199 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=101199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we're trying to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28100%29 ALIGN=MIDDLE  ALT=\"C%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, our test zero is 100\r<BR>\n" );
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document.write( "Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "<TD >1/2</TD>\r\n" );
document.write( "<TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><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 (it is the coefficient with the highest exponent which is 1)\r<BR>\n" );
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document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "<TD >1/2</TD>\r\n" );
document.write( "<TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "<TD >1/2</TD>\r\n" );
document.write( "<TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "Multiply 100 by 1/2 and place the product (which is 50)  right underneath the second  coefficient (which is -8)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "Add 50 and -8 to get 42. Place the sum right underneath 50.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >42</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD></TR>\n" );
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document.write( "Multiply 100 by 42 and place the product (which is 4200)  right underneath the third  coefficient (which is -80)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD >4200</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >42</TD>\r\n" );
document.write( "    <TD >4120</TD>\r\n" );
document.write( "    <TD ></TD></TR>\n" );
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document.write( "Add 4200 and -80 to get 4120. Place the sum right underneath 4200.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD >4200</TD>\r\n" );
document.write( "    <TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >42</TD>\r\n" );
document.write( "    <TD >4120</TD>\r\n" );
document.write( "    <TD ></TD></TR>\n" );
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document.write( "Multiply 100 by 4120 and place the product (which is 412000)  right underneath the fourth  coefficient (which is 200)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD >4200</TD>\r\n" );
document.write( "    <TD >412000</TD>\r\n" );
document.write( "    <TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD>\r\n" );
document.write( "    <TD >42</TD>\r\n" );
document.write( "    <TD >4120</TD>\r\n" );
document.write( "    <TD ></TD></TR>\n" );
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document.write( "Add 412000 and 200 to get 412200. Place the sum right underneath 412000.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >100</TD><TD >|</TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >-8</TD><TD >-80</TD><TD >200</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD>\r\n" );
document.write( "    <TD >50</TD>\r\n" );
document.write( "    <TD >4200</TD>\r\n" );
document.write( "    <TD >412000</TD>\r\n" );
document.write( "    <TD ></TD></TR><TR><TD ></TD><TD ></TD>\r\n" );
document.write( "    <TD >1/2</TD>\r\n" );
document.write( "    <TD >42</TD>\r\n" );
document.write( "    <TD >4120</TD>\r\n" );
document.write( "    <TD >412200</TD>\r\n" );
document.write( "    </TR>\n" );
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document.write( "Since the last column adds to 412200, we have a remainder of 412200. \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So according to the remainder theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28100%29=412200 ALIGN=MIDDLE  ALT=\"C%28100%29=412200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the cost to produce 100 boxes is $412,200 </SPAN>\n" );
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