Factorise $a^{3} + a^{2} + a + 1$.

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

Solution

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

Asked in: IMO

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