Final answer:
The polynomial 16x² + 56x + 49 is a perfect square trinomial and can be factored completely as (4x + 7)².
Step-by-step explanation:
The polynomial given is 16x² + 56x + 49.
First, we look for a common factor, but since there is none other than 1, we check if the polynomial is a perfect square trinomial. To do so, we see that 16x² is a perfect square of 4x, and 49 is a perfect square of 7. Furthermore, twice the product of 4x and 7 gives us 56x, which means the given polynomial is indeed a perfect square trinomial. Hence, it can be factored as:
(4x + 7)²
So the complete factorization of the polynomial 16x² + 56x + 49 is (4x + 7)².