The problem asks us to factor the quadratic expression $36x^2 - 60x + 25$, if possible. We need to select the correct choice below and fill in any answer boxes within your choice. The options are: A) give the factored expression, or B) declare the polynomial is prime.

1. Problem Description

The problem asks us to factor the quadratic expression $36x^2 - 60x + 25$, if possible. We need to select the correct choice below and fill in any answer boxes within your choice. The options are: A) give the factored expression, or B) declare the polynomial is prime.

2. Solution Steps

We need to factor the quadratic expression $36x^2 - 60x + 25$.

We can recognize this as a perfect square trinomial of the form $(ax - b)^2 = a^2x^2 - 2abx + b^2$.

Here, $a^2 = 36$, so $a = 6$. Also, $b^2 = 25$, so $b = 5$.

Then, $2ab = 2(6)(5) = 60$.

Thus, we can write the given expression as $(6x)^2 - 2(6x)(5) + (5)^2 = (6x - 5)^2 = (6x-5)(6x-5)$.

Therefore, $36x^2 - 60x + 25 = (6x-5)^2$.

3. Final Answer

A. $36x^2 - 60x + 25 = (6x-5)^2$