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Quantitative Aptitude :: Simplification - Discussion

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Choose the correct option.

P ( x ) = ( x999 + x998 + x997 + . . . . + x + 1)2 - x999Q ( x ) = x998 + x 997 + . . . . + x + 1The reminder when P ( x ) is divided by Q ( x ) is

Ax + 1

B0

C1

Dx-1

Answer: Option (Login/Signup)

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Solution: ((x^999 x^998 ... x 1)^2-x^999)/(x^998 x^997 ... x 1)



=> ((x^999 x^998 ... x 1)^2-x^999)/(x^999 x^998 ... x 1)-x^999 or,



=>(x^998 ... x 2)^2-1/(x^998 ... x 2)-1 [taking x^999 as common and cancelling it]



we can now use the identity a^2-b^2=(a b)*(a-b)



using this we can see that p(x) is clearly divisible by q(x)



i.e. p(x)/q(x)= (x^999 x^998 ... x 1) x^999



so the remainder will be 0

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