Question

Sum of the coefficient of f(x) if {16x^6-11x+2}f(x) =2016.x^2015​

Answer 1

Given : {16x⁶-11x+2}f(x) =2016.x²⁰¹⁵

To find : Sum of the coefficient of f(x)

Solution:

f(x) =aₙxⁿ + aₙ₋₁xⁿ⁻¹  + . + .  + a₁x  + a₀  

x = 1

=> f(1) = aₙ  + aₙ₋₁   + . + .  + a₁   + a₀  

Hence f(1) = Sum of the coefficient of f(x)

{16x⁶-11x+2}f(x) =2016.x²⁰¹⁵

substitute x = 1

=> {16 -11 +2}f(1) =2016

=> 7f(1) = 2016

=>  f(1) =  288

Sum of the coefficient of f(x)   = 288

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