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