document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44785>Question 44785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a long division problem that I'm having trouble with.  I've tried to follow the book, but can't seem to solve it correctly....please help! Thank you.\r<BR>\n" );
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document.write( "Perform the indicated division...<BR>\n" );
document.write( "(5n^4+28n^3-10n^2+196n-315)divided by (n^2+7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29682 by </B><A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><B>aaaaaaaa(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><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=29682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This will take some time because the polynomials are big, but I'll try to explain it. When long dividing two polynomials, you divide only the first term of the dividend for the first of the divisor (assuming the degrees are ordered from high to low, just like they are here: 4, 3, 2, 1, 0). Then you multiply the result by the whole polynomial, subtract, and repeat, until the degree of the dividend is lower than the degree of the divisor. This is best learned by example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285n%5E4%2B28n%5E3-10n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29 ALIGN=MIDDLE  ALT=\"%285n%5E4%2B28n%5E3-10n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We'll divide first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285n%5E4%29%2F%28n%5E2%29 ALIGN=MIDDLE  ALT=\"%285n%5E4%29%2F%28n%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (always the terms with the highest exponent on both sides of the division). The quotient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2 ALIGN=MIDDLE  ALT=\"5n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > We multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%28n%5E2%2B7%29 ALIGN=MIDDLE  ALT=\"5n%5E2%28n%5E2%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E4+%2B+35n%5E2 ALIGN=MIDDLE  ALT=\"5n%5E4+%2B+35n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We then subtract the result from the dividend to get as our new dividend <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28n%5E3-45n%5E2%2B196n-315 ALIGN=MIDDLE  ALT=\"28n%5E3-45n%5E2%2B196n-315\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285n%5E4%2B28n%5E3-10n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29+=+5n%5E2+%2B+%2828n%5E3-45n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Continuing:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28n%5E3%2Fn%5E2+=+28n ALIGN=MIDDLE  ALT=\"28n%5E3%2Fn%5E2+=+28n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28n%28n%5E2+%2B+7%29+=+28n%5E3+%2B+196n ALIGN=MIDDLE  ALT=\"28n%28n%5E2+%2B+7%29+=+28n%5E3+%2B+196n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%2828n%5E3%29+-+45n%5E2+%2B+cross%28196n%29+-+315%29+-+%28cross%2828n%5E3%29+%2B+cross%28196n%29%29+=+-45n%5E2+-+315 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-45n%5E2%2Fn%5E2+=+-45 ALIGN=MIDDLE  ALT=\"-45n%5E2%2Fn%5E2+=+-45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-45%28n%5E2+%2B+7%29+=+-45n%5E2+-+315 ALIGN=MIDDLE  ALT=\"-45%28n%5E2+%2B+7%29+=+-45n%5E2+-+315\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Fortunately, both terms cancel out and we have no remainder.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-45n%5E2+-+315%29+-+%28-45n%5E2+-+315%29+=+0 ALIGN=MIDDLE  ALT=\"%28-45n%5E2+-+315%29+-+%28-45n%5E2+-+315%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, summing up our quotients:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285n%5E4%2B28n%5E3-10n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29+=+5n%5E2+%2B+28n+-+45 ALIGN=MIDDLE  ALT=\"%285n%5E4%2B28n%5E3-10n%5E2%2B196n-315%29%2F%28n%5E2%2B7%29+=+5n%5E2+%2B+28n+-+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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