document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85751>Question 85751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x^4 - 8x^2 + 6 divided by 2x + 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61981 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=61981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E4+-+8x%5E2+%2B+6%29%2F%282x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x%5E4+-+8x%5E2+%2B+6%29%2F%282x%2B2%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=2x%2B2=0 ALIGN=MIDDLE  ALT=\"2x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2 ALIGN=MIDDLE  ALT=\"2x%2B2\"   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=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
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document.write( "so our test zero is -1\r<BR>\n" );
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document.write( "Now set up the synthetic division table by placing the test zero in the upperleft 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=2x%5E4 ALIGN=MIDDLE  ALT=\"2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%5E2 ALIGN=MIDDLE  ALT=\"-8x%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=2x%5E4+-+8x%5E2+%2B+6 ALIGN=MIDDLE  ALT=\"2x%5E4+-+8x%5E2+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > really looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4%2B0x%5E3%2B-8x%5E2%2B0x%5E1%2B6x%5E0 ALIGN=MIDDLE  ALT=\"2x%5E4%2B0x%5E3%2B-8x%5E2%2B0x%5E1%2B6x%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</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 >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</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 -1 by 2 and place the product (which is -2)  right underneath 0\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</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 -2 and 0 to get -2. Place the sum right underneath -2.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by -2 and place the product (which is 2)  right underneath -8\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 2 and -8 to get -6. Place the sum right underneath 2.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD >-6</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by -6 and place the product (which is 6)  right underneath 0\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD >6</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD >-6</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 6 and 0 to get 6. Place the sum right underneath 6.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD >6</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD >-6</TD><TD >6</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by 6 and place the product (which is -6)  right underneath 6\r<BR>\n" );
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document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD >6</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD >-6</TD><TD >6</TD><TD ></TD></TR>\n" );
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document.write( "    Add -6 and 6 to get 0. Place the sum right underneath -6.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >2</TD><TD >0</TD><TD >-8</TD><TD >0</TD><TD >6</TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD >-2</TD><TD >2</TD><TD >6</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >2</TD><TD >-2</TD><TD >-6</TD><TD >6</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=2x%2B2 ALIGN=MIDDLE  ALT=\"2x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4+-+8x%5E2+%2B+6 ALIGN=MIDDLE  ALT=\"2x%5E4+-+8x%5E2+%2B+6\"   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 4 coefficients (2,-2,-6,6) form the quotient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+2x%5E2+-+6x+%2B+6 ALIGN=MIDDLE  ALT=\"2x%5E3+-+2x%5E2+-+6x+%2B+6\"   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=2x%2B2 ALIGN=MIDDLE  ALT=\"2x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the x term has a coefficient of 2, so we need to divide the quotient by 2 like this:\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=%282x%5E4+-+8x%5E2+%2B+6%29%2F%282x%2B2%29=x%5E3+-+x%5E2+-+3x+%2B+3 ALIGN=MIDDLE  ALT=\"%282x%5E4+-+8x%5E2+%2B+6%29%2F%282x%2B2%29=x%5E3+-+x%5E2+-+3x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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