If f(x) = ${({rm{1 + x + }}{{rm{x}}^2} + {x^3} + .......{x^{2012}})^2} - {x^{2012}}$
g(x) = ${rm{1 + x + }}{{rm{x}}^2} + {x^3} + .......{x^{2011}}$
Then what is the remainder when f(x) is divided by g(x)

• ans-(1-x)..
  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.
  
• 11 years agoHelpfull: Yes(3) No(3)
• ans is 0.....
  
• 11 years agoHelpfull: Yes(2) No(1)
• 0 is the right ans
  
• 11 years agoHelpfull: Yes(2) No(1)
• @piyush can u plz explain the questn?it is nt clear to me...
• 11 years agoHelpfull: Yes(0) No(0)