To factor the quadratic expression \( w^2 + 6w + 8 \), we need to find two numbers that multiply to \( 8 \) (the constant term) and add up to \( 6 \) (the coefficient of the middle term).
The two numbers that meet these criteria are \( 2 \) and \( 4 \), since:
- \( 2 \times 4 = 8 \)
- \( 2 + 4 = 6 \)
Using these numbers, we can factor the expression as follows:
\[ w^2 + 6w + 8 = (w + 2)(w + 4) \]
Thus, the factored form of \( w^2 + 6w + 8 \) is:
\[ (w + 2)(w + 4) \]