1. **State the problem:** Factor the quadratic expression $f^2 + 5f + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. Here, $a=1$, $b=5$, and $c=6$. We need two numbers that multiply to $1 \times 6 = 6$ and add to $5$. 4. The numbers $2$ and $3$ satisfy this because $2 \times 3 = 6$ and $2 + 3 = 5$. 5. Rewrite the middle term using these numbers: $$f^2 + 2f + 3f + 6$$ 6. Group terms: $$(f^2 + 2f) + (3f + 6)$$ 7. Factor each group: $$f(f + 2) + 3(f + 2)$$ 8. Factor out the common binomial: $$(f + 2)(f + 3)$$ **Final answer:** The factorization of $f^2 + 5f + 6$ is $$(f + 2)(f + 3)$$.