Latest TCS Aptitude Question SOLUTION: 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

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(#M40029613) TCS question Keep an EYE

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)

Asked In TCS vishal kumar singh (10 years ago)

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piyush upadhyay  (10 years ago)

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.

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swati  (10 years ago)

ans is 0.....

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vishal kumar singh  (10 years ago)

0 is the right ans

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Pratyusha Bhadra  (10 years ago)

@piyush can u plz explain the questn?it is nt clear to me...

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