1. **Problem 1: Factor the trinomial** $x^2 + 5x + 6$. 2. The general formula for factoring a trinomial of the form $x^2 + bx + c$ is to find two numbers that multiply to $c$ and add to $b$. 3. For $x^2 + 5x + 6$, we look for two numbers that multiply to 6 and add to 5. These numbers are 2 and 3. 4. Therefore, the factors are $(x + 2)(x + 3)$. 5. **Problem 2: Factor the trinomial representing the floor area** $x^2 - 7x - 30$. 6. We need two numbers that multiply to $-30$ and add to $-7$. These numbers are $-10$ and $3$. 7. So, the factors are $(x - 10)(x + 3)$. 8. The length and width of the mosque floor are $x - 10$ and $x + 3$ respectively. **Final answers:** - $x^2 + 5x + 6 = (x + 2)(x + 3)$ - Floor area $x^2 - 7x - 30 = (x - 10)(x + 3)$ with length $x - 10$ and width $x + 3$.