1. **State the problem:** Factor the quadratic expression $x^2 + 4x + 3$. 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, $a=1$, $b=4$, and $c=3$. We need two numbers that multiply to $1 \times 3 = 3$ and add to $4$. 4. The numbers $1$ and $3$ satisfy this because $1 \times 3 = 3$ and $1 + 3 = 4$. 5. Rewrite the middle term using these numbers: $$x^2 + 1x + 3x + 3$$ 6. Group terms: $$(x^2 + 1x) + (3x + 3)$$ 7. Factor each group: $$x(x + 1) + 3(x + 1)$$ 8. Factor out the common binomial: $$(x + 3)(x + 1)$$ **Final answer:** $$\boxed{(x + 3)(x + 1)}$$