1. The first problem is to simplify or factor the expression $x^2 + 6x + 8$. 2. We use the factoring formula for quadratic expressions: $$ax^2 + bx + c = (x + m)(x + n)$$ where $m$ and $n$ satisfy $m + n = b$ and $mn = c$. 3. For $x^2 + 6x + 8$, we look for two numbers that add to 6 and multiply to 8. 4. The numbers 2 and 4 satisfy these conditions because $2 + 4 = 6$ and $2 \times 4 = 8$. 5. Therefore, the factorization is $$x^2 + 6x + 8 = (x + 2)(x + 4).$$ Final answer: $(x + 2)(x + 4)$