The problem asks us to factor the quadratic expression $25x^2 + 60x + 36$ if possible. If the expression cannot be factored, we are to state that the polynomial is prime.

1. Problem Description

The problem asks us to factor the quadratic expression $25x^2 + 60x + 36$ if possible. If the expression cannot be factored, we are to state that the polynomial is prime.

2. Solution Steps

First, we observe that the given expression is a quadratic trinomial. We can attempt to factor it by recognizing it as a perfect square trinomial of the form $(ax + b)^2 = a^2x^2 + 2abx + b^2$.

Here, $a^2 = 25$, $2ab = 60$, and $b^2 = 36$.

Taking the square root of $a^2 = 25$, we get $a = 5$.

Taking the square root of $b^2 = 36$, we get $b = 6$.

Let's check if $2ab = 60$:

$2(5)(6) = 60$. This matches the middle term coefficient.

Therefore, the expression can be factored as $(5x + 6)^2$.

3. Final Answer

$(5x + 6)^2$