To factor the polynomial x² + 12x + 36, we can recognize that it is a trinomial in the standard form of ax² + bx + c. In this case, we have:
- a = 1
- b = 12
- c = 36
One effective method for factoring a trinomial is to look for two numbers that multiply to c (which is 36) and add up to b (which is 12).
The factors of 36 that add up to 12 are 6 and 6 (since 6 × 6 = 36 and 6 + 6 = 12).
Thus, we can rewrite the polynomial as:
(x + 6)(x + 6) or (x + 6)².
In this case, since both factors are the same, we can say that this polynomial is a perfect square trinomial.
So, the factoring method we can consider here is the perfect square trinomial method, which allows us to express x² + 12x + 36 as (x + 6)².