We have: 2006=2005+1=x+12006=2005+1=x+1

Hence B=x2005−2006x2004+2006x2003−...+2006x+1B=x2005−2006x2004+2006x2003−...+2006x+1

=x2005−(x+1)x2004+(x+1)x2003−...+(x+1)x+1=x2005−(x+1)x2004+(x+1)x2003−...+(x+1)x+1

=x2005−x2005−x2004+x2014+x2013−...+x2+x+1=x2005−x2005−x2004+x2014+x2013−...+x2+x+1

=x+1=2005+1=2006