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Probability Level 3

if f ( x ) = x 6 + 10 x 5 + 10 x 4 + 10 x 3 + 10 x 2 + 10 x + 10 f(x)=x^{6}+10x^{5}+10x^{4}+10x^{3}+10x^{2}+10{x} +10 then find f ( 11 ) f(11) .


The answer is 3543121.

Nutan Sinha by Nutan Sinha , 16, India

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1 solution

Rewrite 10 = x − 1 10 = x-1 . Then f ( x ) = x 6 + ( x − 1 ) ( x 5 + x 4 + ⋯ + x 0 ) = x 6 + ( x 6 − 1 ) = 2 x 6 − 1. f(x) = x^6 + (x -1)(x^5 + x^4 + \cdots + x^0) = x^6 + (x^6 - 1)= 2x^6 - 1. Use a calculator for the rest.

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