1. Stating the problem: Simplify or factor the quadratic expression $x^2 + 4x + 3$. 2. To factor, we look for two numbers whose product is $3$ (the constant term) and whose sum is $4$ (the coefficient of $x$). 3. The numbers $1$ and $3$ satisfy these conditions since $1 \times 3 = 3$ and $1 + 3 = 4$. 4. Therefore, the quadratic can be factored as: $$x^2 + 4x + 3 = (x + 1)(x + 3)$$ 5. Final answer: The factored form of $x^2 + 4x + 3$ is $(x + 1)(x + 3)$.