document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133344>Question 133344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide. Use synthetic division if possible<BR>\n" );
document.write( "(8x^4+5x^3+4x^2-x+7)/(x+1)<BR>\n" );
document.write( "(12x^3+31x^2-17x-6)/(x+3)\r<BR>\n" );
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document.write( "i need some major help with these 2 questions. i was given 110 questions, i need some help with these 2=/ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97532 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=97532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\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=%288x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%288x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7%29%2F%28x%2B1%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%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   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 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 >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</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 8)\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</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 >8</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by 8 and place the product (which is -8)  right underneath the second  coefficient (which is 5)\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add -8 and 5 to get -3. Place the sum right underneath -8.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by -3 and place the product (which is 3)  right underneath the third  coefficient (which is 4)\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 3 and 4 to get 7. Place the sum right underneath 3.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD >7</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by 7 and place the product (which is -7)  right underneath the fourth  coefficient (which is -1)\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD >-7</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD >7</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add -7 and -1 to get -8. Place the sum right underneath -7.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD >-7</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD >7</TD><TD >-8</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -1 by -8 and place the product (which is 8)  right underneath the fifth  coefficient (which is 7)\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD >-7</TD><TD >8</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD >7</TD><TD >-8</TD><TD ></TD></TR>\n" );
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document.write( "    Add 8 and 7 to get 15. Place the sum right underneath 8.\r<BR>\n" );
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document.write( "<TR><TD >-1</TD><TD >|</TD><TD >8</TD><TD >5</TD><TD >4</TD><TD >-1</TD><TD >7</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-8</TD><TD >3</TD><TD >-7</TD><TD >8</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >8</TD><TD >-3</TD><TD >7</TD><TD >-8</TD><TD >15</TD></TR>\n" );
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document.write( "Since the last column adds to 15, we have a remainder of 15. This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   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=8x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7 ALIGN=MIDDLE  ALT=\"8x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7\"   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 (8,-3,7,-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=8x%5E3+-+3x%5E2+%2B+7x+-+8 ALIGN=MIDDLE  ALT=\"8x%5E3+-+3x%5E2+%2B+7x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the last coefficient 15, is the remainder, which is placed over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   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=15%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"15%2F%28x%2B1%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=8x%5E3+-+3x%5E2+%2B+7x+-+8%2B15%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"8x%5E3+-+3x%5E2+%2B+7x+-+8%2B15%2F%28x%2B1%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=%288x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7%29%2F%28x%2B1%29=8x%5E3+-+3x%5E2+%2B+7x+-+8%2B15%2F%28x%2B1%29 ALIGN=MIDDLE   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=%288x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7%29%2F%28x%2B1%29=8x%5E3+-+3x%5E2+%2B+7x+-+8 ALIGN=MIDDLE  ALT=\"%288x%5E4+%2B+5x%5E3+%2B+4x%5E2+-+x+%2B+7%29%2F%28x%2B1%29=8x%5E3+-+3x%5E2+%2B+7x+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > remainder 15\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( "# 2\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=%2812x%5E3+%2B+31x%5E2+-+17x+-+6%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%2812x%5E3+%2B+31x%5E2+-+17x+-+6%29%2F%28x%2B3%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%2B3=0 ALIGN=MIDDLE  ALT=\"x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
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document.write( "so our test zero is -3\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 >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</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 12)\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -3 by 12 and place the product (which is -36)  right underneath the second  coefficient (which is 31)\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add -36 and 31 to get -5. Place the sum right underneath -36.\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD >-5</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -3 by -5 and place the product (which is 15)  right underneath the third  coefficient (which is -17)\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD >15</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD >-5</TD><TD ></TD><TD ></TD></TR>\n" );
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document.write( "    Add 15 and -17 to get -2. Place the sum right underneath 15.\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD >15</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD >-5</TD><TD >-2</TD><TD ></TD></TR>\n" );
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document.write( "    Multiply -3 by -2 and place the product (which is 6)  right underneath the fourth  coefficient (which is -6)\r<BR>\n" );
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document.write( "<TR><TD >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD >15</TD><TD >6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD >-5</TD><TD >-2</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 >-3</TD><TD >|</TD><TD >12</TD><TD >31</TD><TD >-17</TD><TD >-6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-36</TD><TD >15</TD><TD >6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >12</TD><TD >-5</TD><TD >-2</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=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E3+%2B+31x%5E2+-+17x+-+6 ALIGN=MIDDLE  ALT=\"12x%5E3+%2B+31x%5E2+-+17x+-+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 3 coefficients (12,-5,-2) form the quotient\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%5E3+%2B+31x%5E2+-+17x+-+6%29%2F%28x%2B3%29=12x%5E2+-+5x+-+2 ALIGN=MIDDLE  ALT=\"%2812x%5E3+%2B+31x%5E2+-+17x+-+6%29%2F%28x%2B3%29=12x%5E2+-+5x+-+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\r<BR>\n" );
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document.write( " </SPAN>\n" );
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