Factorise $x^{3} - 2x^{2} - x + 2$.

Factorise $x^{3} - 2x^{2} - x + 2$.
  1. $(x-2)(x-1)(x+1)$
  2. $(x-2)(x+1)^{2}$
  3. $(x+2)(x-1)(x+1)$
  4. $(x-2)(x^{2}+1)$

Solution

Group: $x^{2}(x-2) - 1(x-2) = (x-2)(x^{2}-1) = (x-2)(x-1)(x+1)$.

Asked in: IMO

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