Final answer:
The polynomial 36x²-84xy+49y² is a perfect square trinomial that can be factored into (6x-7y)².
Step-by-step explanation:
The student asked to factor the polynomial 36x²-84xy+49y² or state that it is prime. This polynomial can be factored because it is a perfect square trinomial. We first look for the square root of the first term, which is 6x, and the square root of the last term, which is 7y. Then we check if twice the product of these two terms is equal to the middle term, and in this case, 2*(6x)*(7y) equals 84xy, which is our middle term with the minus sign. Hence, the factored form of the given polynomial is:
(6x-7y)2
The process of factoring includes identifying perfect squares and understanding how to apply the formula for factoring a difference of squares when necessary.