Practice and apply :Factor each trinomial if it is not factorable .write prime                                           ×²+6×+8

To factor the trinomial \(x^2 + 6x + 8\), we look for two numbers that multiply to give the constant term (8) and add up to give the coefficient of the linear term (6). 

### Step-by-Step Solution

1. **Identify the coefficients:**
   - The trinomial is in the form \(ax^2 + bx + c\), where:
     - \(a = 1\) (coefficient of \(x^2\))
     - \(b = 6\) (coefficient of \(x\))
     - \(c = 8\) (constant term)

2. **Find two numbers that multiply to \(c = 8\) and add up to \(b = 6\):**
   - Possible pairs of factors of 8: \((1, 8), (2, 4)\)
   - The pair that adds up to 6 is \((2, 4)\).

3. **Write the trinomial as a product of two binomials:**
   - Since \(2\) and \(4\) are the numbers we found, we can express the trinomial as:
   \[
   x^2 + 6x + 8 = (x + 2)(x + 4)
   \]

4. **Verify the factorization:**
   - To ensure our factorization is correct, expand \((x + 2)(x + 4)\):
   \[
   (x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
   \]

Since the expansion matches the original trinomial, the factorization is correct.

### Conclusion
The trinomial \(x^2 + 6x + 8\) factors to:
\[
(x + 2)(x + 4)
\]

It is **not prime**.

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### Related Questions
1. How do you factor a trinomial when the coefficient of \(x^2\) is not 1?
2. What are the steps to factor a quadratic trinomial that cannot be easily factored?
3. How do you recognize when a trinomial is a perfect square?
4. What does it mean for a trinomial to be "prime" in mathematics?
5. Can all quadratic trinomials be factored into binomials with real coefficients?

### Tip
When factoring trinomials, always check if the middle term's coefficient can be obtained by adding two factors of the constant term.

Learn how to factor the trinomial x^2 + 6x + 8 with a detailed step-by-step solution. This problem involves factoring quadratic equations and understanding key algebraic concepts. Suitable for students in Grades 9-12.

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