Answer
$(x+3)(x+4)$
Work Step by Step
To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$.
In the case of $x^2+7x+12$, we are looking for two numbers whose product is $12$ and whose sum is $7$. The numbers $3$ and $4$ meet these criteria, because $$3\times4=12\;\text{and}\;3+4=7$$When we insert these numbers into the blanks, we arrive at the factors: $(x+3)(x+4)$.
