It might be a bit more mechanical to use the rational roots theorem tofind -1 and then just do some polynomial divisionx^4 + x^3 + x + 1 | x + 1 = x^3 + 1So the full factorization is:(x+1)(x+1)(x^2 - x + 1) and only the first 2 parts have rational roots.
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It might be a bit more mechanical to use the rational roots theorem to
find -1 and then just do some polynomial division
x^4 + x^3 + x + 1 | x + 1 = x^3 + 1
So the full factorization is:
(x+1)(x+1)(x^2 - x + 1) and only the first 2 parts have rational roots.
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