document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982382>Question 982382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the remainder when (x^9 + 2x^8 + 3x^7 +…+ 9^x) is divided by (x – 1).<BR>\n" );
document.write( "A. 45 C. 180<BR>\n" );
document.write( "B. 90 D. 360 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603229 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polynomial you meant to write is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=x%5E9+%2B+2x%5E8+%2B+3x%5E7+%2B%22...%22%2B8x%5E2%2B9x ALIGN=MIDDLE  ALT=\"P%28x%29=x%5E9+%2B+2x%5E8+%2B+3x%5E7+%2B%22...%22%2B8x%5E2%2B9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "where for each term the power of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the coefficient add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The remainder when a polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29 ALIGN=MIDDLE  ALT=\"P%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=1%2B2%2B3%2B%22...%22%2B8%2B9=highlight%2845%29 ALIGN=MIDDLE  ALT=\"P%281%29=1%2B2%2B3%2B%22...%22%2B8%2B9=highlight%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I could add using pencil and paper, or a calculator,<BR>\n" );
document.write( "but I know that sum to be the sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%289%29 ALIGN=MIDDLE  ALT=\"red%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > consecutive terms of an arithmetic sequence,<BR>\n" );
document.write( "with the first and last of those terms being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%289%29 ALIGN=MIDDLE  ALT=\"green%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=1%2B2%2B3%2B%22...%22%2B8%2Bgreen%289%29=red%289%29%281%2Bgreen%289%29%29%2F2=red%289%29%2A10%2F2=9%2A5=highlight%2845%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );