document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153471>Question 1153471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of n does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3-1%2Fx%29%5En ALIGN=MIDDLE  ALT=\"%282x%5E3-1%2Fx%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, have a non-zero constant term? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775692 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are n factors of (2x^3-1/x).<br><BR>\n" );
document.write( "To get a constant partial product, you need to pick the \"-1/x\" term 3 times as often as you pick the \"2x^3\" term.<br><BR>\n" );
document.write( "That means the number of factors must be a multiple of 4.<br><BR>\n" );
document.write( "ANSWER: The exponent n can be any positive multiple of 4.<br><BR>\n" );
document.write( "Example 1: n=4<br><BR>\n" );
document.write( "The next-to-last term in the expansion is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%284%2C1%29%28%282x%5E3%29%5E1%29%28-1%2Fx%29%5E3+=+%284%29%282x%5E3%29%28-1%2Fx%5E3%29+=+-8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Example 2: n=8<br><BR>\n" );
document.write( "The second from last term in the expansion is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%288%2C2%29%28%282x%5E3%29%5E2%29%28-1%2Fx%29%5E6+=+%2828%29%284x%5E6%29%281%2Fx%5E6%29+=+112 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );