Factor the trinomial completely. $$ x^{2}+6 x+8 $$

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To factor the quadratic trinomial $$ x^{2} + 6x + 8 $$ completely, follow these steps:

1. **Identify the coefficients:**
   - The quadratic trinomial is of the form $$ ax^{2} + bx + c $$, where:
     - $$ a = 1 $$
     - $$ b = 6 $$
     - $$ c = 8 $$

2. **Find two numbers that multiply to $$ c $$ (which is 8) and add up to $$ b $$ (which is 6):**
   - Consider the pairs of factors of 8:
     - $$ 1 \times 8 = 8 $$ (sum is 9)
     - $$ 2 \times 4 = 8 $$ (sum is 6)
   
   - The pair $$ 2 $$ and $$ 4 $$ add up to $$ 6 $$, which is the coefficient of the middle term.

3. **Write the factored form:**
   - Using the numbers $$ 2 $$ and $$ 4 $$, the trinomial can be factored as:
     $$
     (x + 2)(x + 4)
     $$

**Final Answer:**
$$
(x + 2)(x + 4)
$$
$$ (x + 2)(x + 4) $$

Factor the trinomial completely.

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