Question

Factor x^2-6x+9 A.) (x-3) B.) (x-3)(x+3) C.) (x-3)^2 D.) (x+3)^2

Answer 1

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)