If I understood correctly, then I must assign to make it so that $f (x) = f (1)$. But the question arises. How ? Should I simply substitute the value $(1)$ into the place $(x)$ for a general polynomial formula of any degree? Or is there another option?
$f(x)= a_0x^n +a_1x^{n-1}+a_2x^{n-2}+...+a_{n-2}x^2 +a_{n-1}x+a_n$
$f(1)=a_01^n +a_11^{n-1}+a_21^{n-2}+...+a_{n-2}1^2 +a_{n-1}1+a_n$
It seems to me that I am doing something wrong.
If $f(x)= a_0x^n +a_1x^{n-1}+a_2x^{n-2}+...+a_{n-2}x^2 +a_{n-1}x+a_n$
then $f(1)=a_01^n +a_11^{n-1}+a_21^{n-2}+...+a_{n-2}1^2 +a_{n-1}1+a_n$.
But $1^n=1^{n-1}=1^{n-2}=...=1^2=1$ so
$f(1)=a_0 +a_1+a_2+...+a_{n-2} +a_{n-1}+a_n$
i.e., a polynomial evaluated at $1$ is the sum of its coefficients.