The given quadratic expression is:

\[
x^2 + 13x + 12
\]

We can factor this quadratic expression. To do so, we need to find two numbers that multiply to give 12 and add up to 13. These numbers are 1 and 12.

Thus, the factored form is:

\[
(x + 1)(x + 12)
\]

If you want to solve \(x^2 + 13x + 12 = 0\), set each factor equal to zero:

\[
x + 1 = 0 \quad \text{or} \quad x + 12 = 0
\]

Solving these gives:

\[
x = -1 \quad \text{or} \quad x = -12
\]

So, the solutions are \(x = -1\) and \(x = -12\).

Would you like further explanation or details on this?

Here are some related questions to consider:
1. How do you determine if a quadratic can be factored?
2. Can you solve this quadratic using the quadratic formula?
3. What is the significance of the sum and product of the roots in factoring?
4. How can you check if the factored form is correct?
5. What does the graph of this quadratic equation look like?

**Tip:** Always verify your factored form by expanding it back to the original equation.

Learn how to factor and solve the quadratic equation x² + 13x + 12 with step-by-step instructions. This problem involves algebraic techniques, such as factoring and using the zero product property, and is suitable for students in Grades 8-10.

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