\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(P(x) = x^3 - x^2 + x - 1\).
  1. Show that \((x-1)\) is a factor of \(P(x)\).
  2. Hence, fully factorise \(P(x)\) into a product of linear factors over the complex numbers.

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