document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90353>Question 90353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Remainder Theorem to find P(c). P(x) = x4 + 3x2 + 1, c = 3\r<BR>\n" );
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document.write( "I came up with  107 I am not sure this is right?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65574 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=65574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let our test zero equal 3\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.(note: remember if a polynomial goes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E4 ALIGN=MIDDLE  ALT=\"1x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is a zero coefficient for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is simply because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+3x%5E2+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E4+%2B+3x%5E2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > really looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E4%2B0x%5E3%2B3x%5E2%2B0x%5E1%2B1x%5E0 ALIGN=MIDDLE  ALT=\"1x%5E4%2B0x%5E3%2B3x%5E2%2B0x%5E1%2B1x%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><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></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 >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 3 by 1 and place the product (which is 3)  right underneath the second  coefficient (which is 0)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 3 and 0 to get 3. Place the sum right underneath 3.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</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 third  coefficient (which is 3)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 9 and 3 to get 12. Place the sum right underneath 9.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD >12</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 3 by 12 and place the product (which is 36)  right underneath the fourth  coefficient (which is 0)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD >36</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD >12</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 36 and 0 to get 36. Place the sum right underneath 36.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD >36</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD >12</TD><TD >36</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 3 by 36 and place the product (which is 108)  right underneath the fifth  coefficient (which is 1)\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD >36</TD><TD >108</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD >12</TD><TD >36</TD><TD ></TD></TR>\n" );
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document.write( "    Add 108 and 1 to get 109. Place the sum right underneath 108.\r<BR>\n" );
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document.write( "<TR><TD >3</TD><TD >|</TD><TD >1</TD><TD >0</TD><TD >3</TD><TD >0</TD><TD >1</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >3</TD><TD >9</TD><TD >36</TD><TD >108</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >3</TD><TD >12</TD><TD >36</TD><TD >109</TD></TR>\n" );
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document.write( "Since the last column adds to 109, we have a remainder of 109. \r<BR>\n" );
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document.write( "So P(3)=109\r<BR>\n" );
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document.write( "You can use this <a  rel=nofollow HREF=http://calc101.com/webMathematica/long-divide.jsp>online polynomial division calculator</a> to check your work </SPAN>\n" );
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