Factor the following trinomial. \( \begin{array}{l}25 x^{2}+30 x+9 \\ ([?] x+\square)^{2}\end{array} \)

To factor the trinomial \(25x^{2} + 30x + 9\), notice that it can be expressed as a perfect square. It takes the form \((Ax + B)^{2}\). Find \(A\) and \(B\): 1. Coefficient of \(x^{2}\): \(A = \sqrt{25} = 5\). 2. To find \(B\), note that \(2AB = 30\). Thus, \(2 \cdot 5 \cdot B = 30\) gives \(B = 3\). 3. Now, form the square: \((5x + 3)^{2}\). So, \(25x^{2} + 30x + 9 = (5x + 3)^{2}\).