Final answer:
The perfect square trinomial 9x^2+42x+49 is factored as (3x+7)^2, which is option A. This is accomplished by identifying the square roots of the first and last terms and confirming the middle term is twice their product.
Step-by-step explanation:
The provided expression is a perfect square trinomial, which is a special form of a quadratic equation that can be factored into the square of a binomial. To factor the expression 9x2+42x+49, we first identify the square root of the first term, which is 3x, and the square root of the last term, which is 7. The middle term is twice the product of these two square roots.
Using this method, we can factor the trinomial as (3x+7)2. This is because (3x+7)(3x+7) would result in 9x2+21x+21x+49, simplifying to 9x2+42x+49, which is the original expression. Thus, the correct answer is A. (3x+7)2.