To factor the quadratic expression \(x^2 + 5x + 6\), we look for two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the linear term \(x\)).

The factors of 6 that add up to 5 are 2 and 3. Therefore, we can rewrite the expression as:

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

Now, we group the terms:

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

Factor out the greatest common factor from each group:

\[
x(x + 2) + 3(x + 2)
\]

Notice that \((x + 2)\) is a common factor:

\[
(x + 2)(x + 3)
\]

So, the factored form of \(x^2 + 5x + 6\) is:

\[
\boxed{(x + 2)(x + 3)}
\]

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

### Related Questions
1. How do you factor a quadratic expression when the leading coefficient is not 1?
2. What are the methods to solve a quadratic equation?
3. How do you determine the roots of a quadratic equation from its factored form?
4. Can every quadratic expression be factored into real linear factors?
5. What is the relationship between the roots of a quadratic equation and its coefficients?

**Tip:** When factoring quadratics, always check if the quadratic is in standard form \((ax^2 + bx + c)\) and identify if there are simple factors before using more complex methods like completing the square or the quadratic formula.

Learn how to factor the quadratic expression x^2 + 5x + 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratics and the quadratic formula. Suitable for students in Grades 7-9.

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