Question

Find the factors of $a^3+a-3a^2-3$.

Answer 1

We group it as $(a^3+a)-(3a^2+3)$. Thus
$a^3+a-3a^2-3==a(a^2+1)-3(a^2+1)=(a-3)(a^2+1)$
We can also group it as
$a^3+a-3a^2-3=(a^3-3a^2)+(a-3)=a^2(a-3)=(a^2+1)(a-3)$
We get the same factors by different groupings. They are $(a^2+1)$ and $(a-3)$