1. 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 ?

• solution is 0.when we submit 1 instead of x we get(2013)^2-1^2012.it is divided by 2011.(by using a^2-b^2 formula)(2014*2012)/2012.remainder is 0.quotient is 2014.
• 12 years agoHelpfull: Yes(39) No(4)
• remainder will be 2 cause the first one (x^2012+...)^2/(x^2011+.....)=1 and rest portion will also one (like(1/10)remainder 1)
  hence 1+1=2
• 12 years agoHelpfull: Yes(6) No(17)
• substitute 1 in place of X..... because if its true for 1 then generalized form of X will be automatically true. why i have put here only 1 is because its the no. that might reduce my calculation time, but you can't take 0 it will led to undefined solution(you may put any no. as you wish).
  now for P(0)= 2013^2 - 1 , Q(0)=2012 so remainder will always be 0.
• 12 years agoHelpfull: Yes(6) No(2)
• can u explain clearly..plz.,.,.
• 12 years agoHelpfull: Yes(4) No(2)
• Hi meena your answer seems to be correct, but can u explain why we need substitute 1 as default value , is it an easy way to get the answer? could we go for any other procedure to solve this question
• 12 years agoHelpfull: Yes(4) No(2)
• absolutely correct meena ....very gud....
• 12 years agoHelpfull: Yes(2) No(2)
• answer will be 0.
  
  as p(x)= a^2 - b^2
  p(x)= (a-b) (a+b) & (a-b)=Q(x) then the remainder will be 0.
• 12 years agoHelpfull: Yes(1) No(3)