By looking at the factorisation of  guess the number of irreducible polynomials of degree 2 over . Find all the irreducible polynomials of degree 2 over  .

To determine the number of irreducible polynomials of degree 2 over the finite field \( F_3 \), we'll start by factoring \( x^9 - x \) in \( F_3[x] \).

The polynomial \( x^9 - x \) can be rewritten as \( x(x^8 - 1) \). Now, we need to factor \( x^8 - 1 \). Notice that \( x^8 - 1 \) is a difference of squares, which can be factored as \( (x^4 - 1)(x^4 + 1) \). 

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