hollie-griffiths_60bf8be064926
hollie-griffiths_60bf8be064926
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Since A has characteristic 5, 5a = 0 for all a in A. Let m be a positive integer. Then in A[x], x^m + 4 = x^m - 1 = (x - 1)(x^(m - 1) + ••• + x + 1) = (x + 4)(x^(m-1) + ••• + x + 1), showing that x + 4 is a factor of x^m + 4.