document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138657>Question 138657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use synthetic division to find out if x+2 is a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6 ALIGN=MIDDLE  ALT=\"2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101180 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=101180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "In order to find out if x+2 is a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6 ALIGN=MIDDLE  ALT=\"2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can use synthetic division\r<BR>\n" );
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document.write( "So in this case, the 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 >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</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 2)\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</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 >2</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -2 by 2 and place the product (which is -4)  right underneath the second  coefficient (which is 4)\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add -4 and 4 to get 0. Place the sum right underneath -4.\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -2 by 0 and place the product (which is 0)  right underneath the third  coefficient (which is -3)\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 0 and -3 to get -3. Place the sum right underneath 0.\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD >-3</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -2 by -3 and place the product (which is 6)  right underneath the fourth  coefficient (which is -3)\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD >6</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD >-3</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 6 and -3 to get 3. Place the sum right underneath 6.\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD >6</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD >-3</TD><TD >3</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -2 by 3 and place the product (which is -6)  right underneath the fifth  coefficient (which is -6)\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD >6</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD >-3</TD><TD >3</TD><TD ></TD></TR>\n" );
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document.write( "    Add -6 and -6 to get -12. Place the sum right underneath -6.\r<BR>\n" );
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document.write( "<TR><TD >-2</TD><TD >|</TD><TD >2</TD><TD >4</TD><TD >-3</TD><TD >-3</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-4</TD><TD >0</TD><TD >6</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >0</TD><TD >-3</TD><TD >3</TD><TD >-12</TD></TR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Since the last column adds to -12, we have a remainder of -12. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   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=2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6 ALIGN=MIDDLE  ALT=\"2x%5E4+%2B+4x%5E3+-+3x%5E2+-+3x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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