Suppose \(f \) is a polynomial such that \(f(0) = 47, f(1) = 32, f(2) = -13\), and \(f(3)=16 \) . What is the sum of the coefficients of \(f \)?
\(f(x)=ax^4+bx^3+cx^2+dx+e\\ e=47\\ f(x)=ax^4+bx^3+cx^2+dx+47\\ f(1)=a+b+c+d+47=32\\ a+b+c+d=32-47\\ a+b+c+d=-15\\\)
Ths sum of the coefficients is -15
This would be true even if it the leading power was not 4.
Why just a + b + c + d ? , isn't e a coefficient as well ?