The given quadratic expression is:

\[
x^2 + 7x + 12
\]

To factor this expression, we need to find two numbers that multiply to give 12 (the constant term) and add up to give 7 (the coefficient of the linear term).

These two numbers are 3 and 4, since:
- \( 3 \times 4 = 12 \)
- \( 3 + 4 = 7 \)

Thus, the factored form of the quadratic is:

\[
(x + 3)(x + 4)
\]

Would you like further details or have any questions about this process?

Here are 5 related questions to deepen your understanding:
1. How would you solve the equation \(x^2 + 7x + 12 = 0\)?
2. Can you factor the quadratic expression \(x^2 + 8x + 12\)?
3. What are the solutions of the equation \( (x + 3)(x + 4) = 0 \)?
4. How does the quadratic formula apply to this problem?
5. Can you graph the function \( f(x) = x^2 + 7x + 12 \)?

**Tip:** Always check your factors by expanding them back to ensure they match the original quadratic expression.

Learn how to factor the quadratic equation x² + 7x + 12. This problem explains key algebraic concepts such as factoring quadratics using numbers that multiply to the constant term and add to the linear coefficient. Suitable for students in Grades 8-10.

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