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in our original set! Let’s try another example but a little bit harder. A · B = (x²+1)(x²+x+1) = x⁴+x³+x²+x²+1 = x⁴+x³+(1+1)x²+1 = x⁴+x³+1 Unfortunately, x⁴+x³+1 doesn’t exist in our finite field. So what do we do? Cue irreducible polynomials which are defined as polynomials which can’t be broken