Chapter 5 - Polynomials and Polynomial Functions - 5-1 Polynomial Functions - Practice and Problem-Solving Exercises - Page 287: 69

$x^2+7x+12=(x+4)(x+3)$

The leading coefficient is 1. Thus, to factor the trinomial, just look for factors of 12 whose sum is equal to the coefficient of the middle term. Note that $12=4(3) \text{ and } 4+3=7$. Therefore, the factored form of the trinomial is $(x+4)(x+3)$.