Sum of Coeffeicient

Algebra Level 2

The sum of all the coefficients of ( 11 x 10 ) 2018 (11x-10)^{2018}


The answer is 1.

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1 solution

Jacopo Piccione
Sep 13, 2018

Given a generic polynomial p ( x ) = a n x n + a n 1 x n 1 + . . . + a 1 x + a 0 p(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0 ,

we notice that p ( 1 ) = a n + a n 1 + . . . + a 1 + a 0 p(1)=a_n+a_{n-1}+...+a_1+a_0

which is exactly the sum of coefficients.

In this case: p ( 1 ) = ( 11 1 10 ) 2018 = 1 p(1)=(11\cdot 1-10)^{2018} =\boxed{1}

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