document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995916>Question 995916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help is urgently needed.\r<BR>\n" );
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document.write( "Find the remainder when  x^100 + 2x^99 +3x^98 +... 100x  is divided by <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;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614544 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> synthetic division<BR>\n" );
document.write( "1/1+2+3+4+5...<BR>\n" );
document.write( " =1+1<BR>\n" );
document.write( "===3 +3<BR>\n" );
document.write( "======<BR>\n" );
document.write( "=====6 +4<BR>\n" );
document.write( "The first four terms are<BR>\n" );
document.write( "x^99+3x^98+6x^97+10x^96+...<BR>\n" );
document.write( "The coefficient of each term is the sum of all the preceding terms plus the coefficient of the next term.<BR>\n" );
document.write( "The pattern will be 15,21,28,36.45.55.....<BR>\n" );
document.write( "The coefficient of the 100th term is the sum of the preceding 99 terms plus the coefficient of the 100th term (100), so the quotient will be dividing x-1 into 4950x+100x or 5050 x.<BR>\n" );
document.write( "That will go in 5050 times, and  we subtract  5050x-5050, so that the remainder is 5050.<BR>\n" );
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