Question

Factor x2 -12x + 36

(x + 6)(x - 6)

(x + 6)2

(x - 6)2

(x - 18)2


Can someone help?

Answer 1

(x -6)²

Explanation:

It is worth remembering the form of the square of a binomial:

(a +b)² = a² +2ab +b²

Note that if "a" and "b" have different signs, the middle term will be negative.

In your case, the square root of the constant is half the magnitude of the x-coefficient, so the trinomial you have is a perfect square. Since you just found √36 = 6, and the sign of 12 tells you the terms have different signs, you know the answer is ...

x² -12x +36 = (x -6)²

_____

Of course, you recognize (x +6)(x -6) as the factoring of the difference of squares ...

x² -6² = x² -36

which is not what you have.