To factor the polynomial x² + 12x + 36, we can recognize that it takes the form of a trinomial. A trinomial can often be factored using various methods, but in this case, we can employ the method of perfect square trinomials.
A perfect square trinomial has the general form (a + b)² = a² + 2ab + b². In this case, we can see that:
- a² corresponds to x² (where a = x),
- b² corresponds to 36 (where b = 6 since 6² = 36),
- and 2ab gives us 12x (as 2 * x * 6 = 12x).
Since we have confirmed that our polynomial fits the pattern for a perfect square trinomial, we can factor it as follows:
x² + 12x + 36 = (x + 6)².
This shows that the polynomial can be factored efficiently using the perfect square trinomial method, yielding a clean and simple factorization.