How to write a polynomial in mod p Consider the polynomial $ \ x^3 - 3\ x^2 +2\ x -1$
How can this polynomial be written in mod 3 ?
What confuses me is that I thought we don't change any power . If we have to also consider the powers then will the leading coefficient be equal to zero then.


What confuses me is that I thought we don't change any power . If we have to also consider the powers then will the leading coefficient be equal to zero then.

Your first thought is correct: we don't change any power. Even though $3$ is in the exponent, we don't take the exponents mod 3, but only the coefficients.
So, taking a polynomial mod 3 just means taking each coefficient mod 3 (and leaving the exponents). For example, $6x^3 + 4x^2 - 2 \mod 3$ would be $0x^3 + x^2 + 1$, which is the same as $x^2 + 1$ since we can drop $0$s. This is because $6 \mod 3$ is $0$, $4 \mod 3$ is $1$, and $-2 \mod 3$ is $1$.
