Latest TCS Aptitude Question SOLUTION: 15)p(x)=((x^2012)+(x^2011)+(x^2010)+…………..+x+1)^2-x^2012 Q(x)=((x^2011)+(x^2010)+……………………+x+1).The remainder

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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

Asked In TCS vivaksha solanki (11 years ago)

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s.jaweed hussain  (11 years ago)

2013^2-2011^2/2012=0 ,.....so 0 remainder

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Yamini Joshi  (11 years ago)

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.

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deviprasad gullipalli  (11 years ago)

4 example take x=1
p=3
q=2
remainder=1

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divyang  (10 years ago)

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

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