document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104510>Question 104510</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/061849281x/algebrahomeworkh>College Algebra: Concepts and Models</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 4x^3-x^2-13x+10 divided by 4x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76048 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=76048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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=%284x%5E3+-+x%5E2+-+13x+%2B+10%29%2F%284x-5%29 ALIGN=MIDDLE  ALT=\"%284x%5E3+-+x%5E2+-+13x+%2B+10%29%2F%284x-5%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=4x-5=0 ALIGN=MIDDLE  ALT=\"4x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5 ALIGN=MIDDLE  ALT=\"4x-5\"   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=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
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document.write( "so our test zero is 5/4\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 >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</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 4)\r<BR>\n" );
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document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 5/4 by 4 and place the product (which is 5)  right underneath the second  coefficient (which is -1)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 5 and -1 to get 4. Place the sum right underneath 5.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD >4</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply 5/4 by 4 and place the product (which is 5)  right underneath the third  coefficient (which is -13)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD >5</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD >4</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 5 and -13 to get -8. Place the sum right underneath 5.\r<BR>\n" );
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document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD >5</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD >4</TD><TD >-8</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "    Multiply 5/4 by -8 and place the product (which is -10)  right underneath the fourth  coefficient (which is 10)\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD >5</TD><TD >-10</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD >4</TD><TD >-8</TD><TD ></TD></TR>\n" );
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document.write( "    Add -10 and 10 to get 0. Place the sum right underneath -10.\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >5/4</TD><TD >|</TD><TD >4</TD><TD >-1</TD><TD >-13</TD><TD >10</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >5</TD><TD >5</TD><TD >-10</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >4</TD><TD >4</TD><TD >-8</TD><TD >0</TD></TR>\n" );
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document.write( "Since the last column adds to zero, we have a remainder of zero. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5 ALIGN=MIDDLE  ALT=\"4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+x%5E2+-+13x+%2B+10 ALIGN=MIDDLE  ALT=\"4x%5E3+-+x%5E2+-+13x+%2B+10\"   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 3 coefficients (4,4,-8) form the quotient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+%2B+4x+-+8 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B+4x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice in the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5 ALIGN=MIDDLE  ALT=\"4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the x term has a coefficient of 4, so we need to divide the quotient by 4 like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2+%2B+4x+-+8%29%2F2=x%5E2+%2B+x+-+2 ALIGN=MIDDLE  ALT=\"%284x%5E2+%2B+4x+-+8%29%2F2=x%5E2+%2B+x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E3+-+x%5E2+-+13x+%2B+10%29%2F%284x-5%29=x%5E2+%2B+x+-+2 ALIGN=MIDDLE  ALT=\"%284x%5E3+-+x%5E2+-+13x+%2B+10%29%2F%284x-5%29=x%5E2+%2B+x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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<BR>\n" );
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