The rational roots theorem tells you that if there are any linear rational roots they must be either (x + 1) or (x - 1). If you try dividing (x^4) - (x^3) + (x^2) - (x) + 1 by each of these possibilities you get a remainder both times, so there is no rational linear factor.
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The rational roots theorem tells you that if there are any linear rational roots they must be either (x + 1) or (x - 1). If you try dividing (x^4) - (x^3) + (x^2) - (x) + 1 by each of these possibilities you get a remainder both times, so there is no rational linear factor.