To factorize the quadratic expression x2 + 4x + 3:

To factorize the quadratic expression $x^2 + 4x + 3$:

• Step 1: Identify coefficients. This is a quadratic expression in the form $ax^2 + bx + c$, where $a=1$, $b=4$, and $c=3$.

• Step 2: Find two numbers. We need to find two numbers that multiply to $c$ (which is 3) and add up to $b$ (which is 4). The numbers are 1 and 3, because $1 \times 3 = 3$ and $1 + 3 = 4$.

• Step 3: Write the factored form. Using these two numbers, we can write the expression in factored form.

  $$(x+1)(x+3)$$

• Final Answer: The factored form of $x^2 + 4x + 3$ is $\boxed{(x+1)(x+3)}$.