To factor the quadratic expression \( x^2 + 5x + 6 \), we need to find two numbers that multiply to the constant term (6) and add to the coefficient of the linear term (5).
The two numbers that satisfy these conditions are 2 and 3 since:
- \( 2 \times 3 = 6 \)
- \( 2 + 3 = 5 \)
Now we can write the factored form of the expression:
\[ x^2 + 5x + 6 = (x + 2)(x + 3) \]
So, \( x^2 + 5x + 6 \) factors to \( (x + 2)(x + 3) \).