The given quadratic expression is:

\[
x^2 + 5x + 6
\]

To factor this, we need to find two numbers that multiply to \(6\) (the constant term) and add up to \(5\) (the coefficient of \(x\)).

Those numbers are \(2\) and \(3\), because:

\[
2 \times 3 = 6 \quad \text{and} \quad 2 + 3 = 5
\]

Thus, we can factor the expression as:

\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

This is the factored form of the quadratic expression.

Would you like more details on this? Here are five related questions to further explore:

1. How do you solve quadratic equations by factoring?
2. What is the quadratic formula and when is it used?
3. Can all quadratics be factored easily?
4. How can you check if a quadratic is factorable?
5. How do you find the roots of a factored quadratic equation?

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

Discover how to factor the quadratic expression x² + 5x + 6 using basic algebraic techniques. This step-by-step guide explains how to find factors and check your work, perfect for students in Grades 8-10.

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