1. The problem is to factor the quadratic expression $$x^2 + 5x + 6$$. 2. We look for two numbers that multiply to the constant term 6 and add up to the coefficient of the linear term 5. 3. The pairs of factors of 6 are (1,6) and (2,3). 4. Among these, 2 and 3 add up to 5. 5. Therefore, we can write the factorization as: $$x^2 + 5x + 6 = (x + 2)(x + 3)$$. 6. This is the fully factored form of the quadratic expression.