#### Answer

$(p+8)(p-5)$

#### 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 $p^2+3p-40$, we are looking for two numbers whose product is $-40$ and whose sum is $3$. The numbers $8$ and $-5$ meet these criteria, because:$$8\times(-5)=-40\;\text{and}\;8+(-5)=3$$When we insert these numbers into the blanks, we arrive at the factors: $(p+8)(p-5)$.