document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194080>Question 194080</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>Saxon Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14, then P(3) = ?<BR>\n" );
document.write( "...is it 682?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145675 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=145675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two ways to do this:\r<BR>\n" );
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document.write( "Direct Substitution and Evaluation Method:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=3x%5E5-8x%5E4%2B3x%5E3%2B2x%5E2-16x%2B14 ALIGN=MIDDLE  ALT=\"P%28x%29=3x%5E5-8x%5E4%2B3x%5E3%2B2x%5E2-16x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29=3%283%29%5E5-8%283%29%5E4%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=3%283%29%5E5-8%283%29%5E4%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   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%283%29=3%28243%29-8%283%29%5E4%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=3%28243%29-8%283%29%5E4%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the 5th power to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=243 ALIGN=MIDDLE  ALT=\"243\"   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%283%29=3%28243%29-8%2881%29%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=3%28243%29-8%2881%29%2B3%283%29%5E3%2B2%283%29%5E2-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the 4th power to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   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%283%29=3%28243%29-8%2881%29%2B3%2827%29%2B2%283%29%5E2-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=3%28243%29-8%2881%29%2B3%2827%29%2B2%283%29%5E2-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   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%283%29=3%28243%29-8%2881%29%2B3%2827%29%2B2%289%29-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=3%28243%29-8%2881%29%2B3%2827%29%2B2%289%29-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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%283%29=729-8%2881%29%2B3%2827%29%2B2%289%29-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=729-8%2881%29%2B3%2827%29%2B2%289%29-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=243 ALIGN=MIDDLE  ALT=\"243\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=729 ALIGN=MIDDLE  ALT=\"729\"   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%283%29=729-648%2B3%2827%29%2B2%289%29-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=729-648%2B3%2827%29%2B2%289%29-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-648 ALIGN=MIDDLE  ALT=\"-648\"   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%283%29=729-648%2B81%2B2%289%29-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=729-648%2B81%2B2%289%29-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   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%283%29=729-648%2B81%2B18-16%283%29%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=729-648%2B81%2B18-16%283%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   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%283%29=729-648%2B81%2B18-48%2B14 ALIGN=MIDDLE  ALT=\"P%283%29=729-648%2B81%2B18-48%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   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%283%29=146 ALIGN=MIDDLE  ALT=\"P%283%29=146\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "OR....\r<BR>\n" );
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document.write( "Synthetic Division Method:\r<BR>\n" );
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document.write( "First lets find our test zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
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document.write( "so our test zero is 3\r<BR>\n" );
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document.write( "Now set up a synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the function to the right of the test zero.<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><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><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 3)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 3 by 3 and place the product (which is 9)  right underneath the second  coefficient (which is -8)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 9 and -8 to get 1. Place the sum right underneath 9.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 3 by 1 and place the product (which is 3)  right underneath the third  coefficient (which is 3)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 3 and 3 to get 6. Place the sum right underneath 3.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 3 by 6 and place the product (which is 18)  right underneath the fourth  coefficient (which is 2)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 18 and 2 to get 20. Place the sum right underneath 18.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD >20</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 3 by 20 and place the product (which is 60)  right underneath the fifth  coefficient (which is -16)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD >60</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD >20</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Add 60 and -16 to get 44. Place the sum right underneath 60.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD >60</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD >20</TD><TD >44</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 3 by 44 and place the product (which is 132)  right underneath the sixth  coefficient (which is 14)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD >60</TD><TD >132</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD >20</TD><TD >44</TD><TD ></TD></TR>\n" );
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document.write( "    Add 132 and 14 to get 146. Place the sum right underneath 132.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >3</TD><TD >-8</TD><TD >3</TD><TD >2</TD><TD >-16</TD><TD >14</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >9</TD><TD >3</TD><TD >18</TD><TD >60</TD><TD >132</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >3</TD><TD >1</TD><TD >6</TD><TD >20</TD><TD >44</TD><TD >146</TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "Since the last column adds to 146, we have a remainder of 146. \r<BR>\n" );
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document.write( "So according to the remainder theorem, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29=146 ALIGN=MIDDLE  ALT=\"P%283%29=146\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );