A Pre-RMO question! -10

Algebra Level 2

If p ( y ) p(y) is a polynomial and if ( 15 y 15 − 11 y + 1 ) p ( y ) = 2005 y 2005 (15y^{15}-11y+1)p(y)=2005y^{2005} then find the sum of all the coefficients and the constant term in p ( y ) p(y)

Note: In original problem it was mentioned the unit digit of the sum of the coefficients


The answer is 401.

Zakir Husain by Zakir Husain , 41, India

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1 solution

Ron Gallagher
Jun 4, 2020

For any polynomial function p, p(1) is the sum of all of the coefficients and the constant term. Substituting y = 1 into the formula gives:

5*p(1) = 2005

p(1) = 2005/5 = 401

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