document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133368>Question 133368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I used the problem provided to try to get the answer. I would like to know if this is correct using the synthetic division method.\r<BR>\n" );
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document.write( "(5x^2+34y+24)/ (y-2)\r<BR>\n" );
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document.write( "2   5  34  24<BR>\n" );
document.write( "       10  88<BR>\n" );
document.write( "    5  44  112     5y+44y+24  112/y+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97551 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=97551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This expression MUST have one variable if you want to use a simple form of synthetic division here. So I'm assuming that the expression is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ax%5E2%2B34%2Ax%2B24%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%285%2Ax%5E2%2B34%2Ax%2B24%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's simplify this expression using synthetic division\r<BR>\n" );
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document.write( "Start with the given expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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-2=0 ALIGN=MIDDLE  ALT=\"x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   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=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
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document.write( "so our test zero is 2\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 >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><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 5)\r<BR>\n" );
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document.write( "<TR><TD >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >5</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 2 by 5 and place the product (which is 10)  right underneath the second  coefficient (which is 34)\r<BR>\n" );
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document.write( "<TR><TD >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >10</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >5</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 10 and 34 to get 44. Place the sum right underneath 10.\r<BR>\n" );
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document.write( "<TR><TD >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >10</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >5</TD><TD >44</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 2 by 44 and place the product (which is 88)  right underneath the third  coefficient (which is 24)\r<BR>\n" );
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document.write( "<TR><TD >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >10</TD><TD >88</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >5</TD><TD >44</TD><TD ></TD></TR>\n" );
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document.write( "    Add 88 and 24 to get 112. Place the sum right underneath 88.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >5</TD><TD >34</TD><TD >24</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >10</TD><TD >88</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >5</TD><TD >44</TD><TD >112</TD></TR>\n" );
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document.write( "Since the last column adds to 112, we have a remainder of 112. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+%2B+34x+%2B+24 ALIGN=MIDDLE  ALT=\"5x%5E2+%2B+34x+%2B+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the bottom row of coefficients:\r<BR>\n" );
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document.write( "The first 2 coefficients (5,44) form the quotient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+44 ALIGN=MIDDLE  ALT=\"5x+%2B+44\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the last coefficient 112, is the remainder, which is placed over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=112%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"112%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Putting this altogether, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+44%2B112%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"5x+%2B+44%2B112%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29=5x+%2B+44%2B112%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29=5x+%2B+44%2B112%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which looks like this in remainder form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29=5x+%2B+44 ALIGN=MIDDLE  ALT=\"%285x%5E2+%2B+34x+%2B+24%29%2F%28x-2%29=5x+%2B+44\"   DISABLED_style= \"max-width:90%; height:auto;\" > remainder 112\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\r<BR>\n" );
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document.write( " </SPAN>\n" );
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