Considering the bytes 10001001 and 10101010 as elements of the field F2[X]/hg(X)i, where g(X) is the polynomial X 8 +X 4 +X 3 +X +1, find their product and quotient .

To perform arithmetic operations in the field \(F_2[X]/\langle g(X) \rangle\), where \(g(X) = X^8 + X^4 + X^3 + X + 1\), we'll use polynomial arithmetic modulo \(g(X)\). This means that after each operation, we need to reduce the result modulo \(g(X)\).

Let's denote the given polynomials as \(A(X) = 10001001\) and \(B(X) = 10101010\). We'll perform polynomial multiplication and division in the given field.

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