Final answer:
Factor out a 3 from the original expression, then apply the difference of squares formula to factor the expression completely into 3(6 - x)(6 + x).
Step-by-step explanation:
To factor the expression 108 - 3x^2 completely, we first identify common factors. Here, we can factor out a 3 to get 3(36 - x^2). Notice that 36 - x^2 is a difference of squares, which factors as (6 - x)(6 + x). Therefore, the fully factored form of the given expression is 3(6 - x)(6 + x).