4.7. We consider the field GF (24 ), with P(x) = x4 + x + 1 being the irreducible polynomial. Find the inverses of A(x) = x and B(x) = x2 + x. You can find the inverses either by trial and error, i.e., brute-force search, or by applying the Euclidean algorithm for polynomials. (However, the Euclidean algorithm is only sketched in this chapter.) Verify your answer by multiplying the inverses you determined by A and B, respectively.