Factor Quadratic 54C0Ec

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 9$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored as $(x + m)(x + n)$ where $m$ and $n$ satisfy $m + n = b$ and $mn = c$. 3. **Identify coefficients:** Here, $a = 1$, $b = 6$, and $c = 9$. 4. **Find two numbers:** We need two numbers $m$ and $n$ such that: $$m + n = 6$$ $$mn = 9$$ 5. **Check possible pairs:** The pairs that multiply to $9$ are $(1, 9)$ and $(3, 3)$. Only $(3, 3)$ adds up to $6$. 6. **Write the factorization:** Therefore, $$x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2$$ 7. **Final answer:** The factored form is $\boxed{(x + 3)^2}$.