Factor x^2-6x+9

A.) (x-3)

B.) (x-3) (x+3)

C.) (x-3) ^2

D.) (x+3) ^2

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)