To factor the expression $x^2 + 7x + 12$, we look for two numbers that multiply to $12$ (the constant term) and add up to $7$ (the coefficient of $x$).

Step 1: Find Two Numbers That Multiply to $12$ and Add to $7$

The two numbers that satisfy these conditions are $3$ and $4$ because: $3 \cdot 4 = 12 \quad \text{and} \quad 3 + 4 = 7$

Step 2: Write the Expression as a Product of Two Binomials

Using these numbers, we can factor the expression as: $x^2 + 7x + 12 = (x + 3)(x + 4)$

Final Answer

The factored form of the expression is:

$(x + 3)(x + 4)$

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you factor $x^2 + 8x + 15$?
2. What are the steps for factoring $x^2 + 6x + 9$?
3. How can you check if your factorization is correct?
4. What happens if the middle term coefficient is negative, like in $x^2 - 7x + 12$?
5. How would you factor $x^2 + 5x + 6$?

Tip: When factoring trinomials, look for two numbers that multiply to the constant term and add up to the middle term's coefficient.