Answer:
Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor. When we completely factor, the coefficient of the variable of at least one factor should be 1.
The given expression can be first factored using FOIL.
(a2 + 2)(a2 - 3)
Note that (a2 - 3) can be factored. Think of it as a difference in perfect squares. So in the end, we have
(a2 + 2)(a - √3)(a + √3)