document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134154>Question 134154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I still need help:<BR>\n" );
document.write( "please help me solve the following synthetic division i am struggling with<BR>\n" );
document.write( "Use synthetic division and the remainder theroem to find the indicated function value.\r<BR>\n" );
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document.write( "f(x)=6x to the 4th power +11x³+6x²-6x+53; f(4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98139 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=98139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find f(4), we can use synthetic division with the test zero of 4\r<BR>\n" );
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document.write( "First 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 >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</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 6)\r<BR>\n" );
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document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</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 >6</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 4 by 6 and place the product (which is 24)  right underneath the second  coefficient (which is 11)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 24 and 11 to get 35. Place the sum right underneath 24.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 4 by 35 and place the product (which is 140)  right underneath the third  coefficient (which is 6)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 140 and 6 to get 146. Place the sum right underneath 140.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD >146</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 4 by 146 and place the product (which is 584)  right underneath the fourth  coefficient (which is -6)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD >584</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD >146</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 584 and -6 to get 578. Place the sum right underneath 584.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD >584</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD >146</TD><TD >578</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 4 by 578 and place the product (which is 2312)  right underneath the fifth  coefficient (which is 53)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD >584</TD><TD >2312</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD >146</TD><TD >578</TD><TD ></TD></TR>\n" );
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document.write( "    Add 2312 and 53 to get 2365. Place the sum right underneath 2312.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >4</TD><TD >|</TD><TD >6</TD><TD >11</TD><TD >6</TD><TD >-6</TD><TD >53</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >24</TD><TD >140</TD><TD >584</TD><TD >2312</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >6</TD><TD >35</TD><TD >146</TD><TD >578</TD><TD >2365</TD></TR>\n" );
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document.write( "Since the last column adds to 2365, we have a remainder of 2365. \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=2365 ALIGN=MIDDLE  ALT=\"f%284%29=2365\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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