15)p(x)=((x^2012)+(x^2011)+(x^2010)+…………..+x+1)^2-x^2012
Q(x)=((x^2011)+(x^2010)+……………………+x+1).The remainder when p(x) is divided by Q(X) is
a)1 b)0 c)x+1 d)x-1

• 2013^2-2011^2/2012=0 ,.....so 0 remainder
  
• 12 years agoHelpfull: Yes(7) No(0)
• Let us multiply g(x) with x on the both sides
  x.g(x) = x+x2+x3+.......x2012
  add 1 on both sides
  x. g(x) + 1 = 1+x+x2+x3+.......x2012
  Substitute this value in f(x)
  then f(x) = (x.g(x)+1)2−x2012
  f(x) = x2.g(x)2+2.g(x)+1−x2012
  Now f(x) is divisible by g(x) first two terms are exactly divisible by g(x) and we get 1 - x2012
  But 1 - x2012 = (1 - x)(1+x+x2+x3+.......x2011)
  if this expression is divisible by g(x) we get (1 -x) as remainder.
  
• 12 years agoHelpfull: Yes(2) No(10)
• 4 example take x=1
  p=3
  q=2
  remainder=1
  
• 12 years agoHelpfull: Yes(0) No(1)
• take x=1
  so p(x)= (2012^2)-1
  q(x)= 2011
  so p(x)/q(x)=((2012^2)-1)/2011
  =(((2011+1)^2)-1)/2011
  =(((n+1)-1)^2)/n
  =(n^2 - 2n)/n
  =(n(n-2))/n =n-2
  so remainder =0
• 11 years agoHelpfull: Yes(0) No(0)