Answer
$(p+6)(p+2)$
Work Step by Step
To factor a trinomial in the form $p^2+px+c$, 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 $(p+\_)(p+\_)$.
In the case of $p^2+8p+12$, we are looking for two numbers whose product is $12$ and whose sum is $8$. The numbers $6$ and $2$ meet these criteria because: $$6\times(2)=12\;\text{and}\;6+(2)=8$$When we insert these numbers into the blanks, we arrive at the factors: $(p+6)(p+2)$.
