Factor x2 -12x + 36

Mathematics

1 answer:

zhannawk [14.2K]2 years ago

4 0

Answer:

(x -6)²

Step-by-step 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.

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