There must be two binomial factors. Thus, we eliminate Answer A, which contains only one such factor.
(x-3)(x+3) has the form (a-b)(a+b), which equals a^2 - 3^2. This is a special product. Eliminate Answer B, because a^2 - 3^2 does not equal x^2 - 6x + 9.
The middle term of x^2 - 6x + 9 is negative. This quadratic has the form x^2 - y^2, which is special product and whose factors are (x-y) and (x-y).
Thus, x^2-6x+9 = (x-3)(x-3) (Answer C)