document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172908>Question 172908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x^4 -2x^3 + 5x^2 + x + 1; x^2+2x\r<BR>\n" );
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document.write( "Please explain step by step\r<BR>\n" );
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document.write( "I would really appreciate any help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127767 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=127767\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that you want to do long division right?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E4-2x%5E3%2B5x%5E2%2Bx%2B1%29%2F%28x%5E2%2B2x%29 ALIGN=MIDDLE  ALT=\"%283x%5E4-2x%5E3%2B5x%5E2%2Bx%2B1%29%2F%28x%5E2%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Rewrite the expression like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/1.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now the question is: How many times does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > go into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E4 ALIGN=MIDDLE  ALT=\"3x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "It goes in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times. So place <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > over the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/2.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x ALIGN=MIDDLE  ALT=\"x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E4%2B6x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E4%2B6x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reverse the signs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E4%2B6x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E4%2B6x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E4-6x%5E3 ALIGN=MIDDLE  ALT=\"-3x%5E4-6x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (place this underneath the dividend)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/3.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now Add to get:\r<BR>\n" );
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document.write( "======================================================================\r<BR>\n" );
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document.write( "Now the question is now: How many times does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > go into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%5E3 ALIGN=MIDDLE  ALT=\"-8x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "It goes in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x ALIGN=MIDDLE  ALT=\"-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > times. Place this term over <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the dividend.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/5.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now multiply -8x by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x ALIGN=MIDDLE  ALT=\"x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%5E3-16x%5E2 ALIGN=MIDDLE  ALT=\"-8x%5E3-16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reverse the signs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%5E3-16x%5E2 ALIGN=MIDDLE  ALT=\"-8x%5E3-16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B16x%5E2 ALIGN=MIDDLE  ALT=\"8x%5E3%2B16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (place this underneath the last polynomial)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/6.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now add to get:\r<BR>\n" );
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document.write( "Now how many times does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > go into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x%5E2 ALIGN=MIDDLE  ALT=\"21x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "It goes in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > times. Place this over the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the dividend.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/8.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now multiply 21 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x ALIGN=MIDDLE  ALT=\"x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x%5E2%2B42x ALIGN=MIDDLE  ALT=\"21x%5E2%2B42x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reverse the signs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x%5E2%2B42x ALIGN=MIDDLE  ALT=\"21x%5E2%2B42x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21x%5E2-42x ALIGN=MIDDLE  ALT=\"-21x%5E2-42x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/9.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now add to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/10-2.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > does NOT go into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-41x%2B1 ALIGN=MIDDLE  ALT=\"-41x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that the long division process stops.\r<BR>\n" );
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document.write( "So the quotient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-8x%2B21 ALIGN=MIDDLE  ALT=\"3x%5E2-8x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-41x%2B1 ALIGN=MIDDLE  ALT=\"-41x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E4-2x%5E3%2B5x%5E2%2Bx%2B1%29%2F%28x%5E2%2B2x%29=3x%5E2-8x%2B21%2B%28-41x%2B1%29%2F%28x%5E2%2B2x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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