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The method is the same.
Yes.
The signed integer range extends only from negative infinity to positive infinity. You have to make up your own names and symbols for whole numbers that are not included in that range.
Signed integer is any integer that carries negative sign while unsigned integer is any integer that carries positive sign
f(x) = a0 + a1x + a2x2 + a3x3 + ... + anxn for some integer n, and constants a0, a1, ... an.