To factor the quadratic expression \(x^2 + 6x + 8\), we follow these steps:

1. **Find two numbers that multiply to the constant term (8)** and add up to the coefficient of the linear term (6).

   The two numbers are **2 and 4**, because:
   \[
   2 \times 4 = 8 \quad \text{(product of the constant term)}
   \]
   \[
   2 + 4 = 6 \quad \text{(sum of the coefficient of the linear term)}
   \]

2. **Rewrite the quadratic expression** as:
   \[
   x^2 + 2x + 4x + 8
   \]

3. **Factor by grouping**:
   \[
   x(x + 2) + 4(x + 2)
   \]

4. **Factor out the common binomial**:
   \[
   (x + 2)(x + 4)
   \]

Thus, the factors of \(x^2 + 6x + 8\) are:
\[
(x + 2)(x + 4)
\]

Let me know if you'd like further details or explanations!

Here are some related questions:
1. What is the factored form of \(x^2 + 7x + 12\)?
2. How do you factor a quadratic when the coefficient of \(x^2\) is not 1?
3. Can all quadratics be factored easily? If not, what methods can be used?
4. How do you check if the factors of a quadratic are correct?
5. What is the relationship between factoring and solving quadratic equations?

**Tip**: When factoring quadratics, always check for a greatest common factor (GCF) first before applying other factoring techniques.

Learn how to factor the quadratic expression x^2 + 6x + 8 with a step-by-step solution. This tutorial covers algebraic techniques like factoring by grouping and applying the zero product property. Perfect for students in Grades 8-10.

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