Answer
$(n+2)(n-5)$
Work Step by Step
To factor a trinomial in the form $n^2+bn+c$, 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 $(n+\_)(n+\_)$.
In the case of $n^2-3n-10$, we are looking for two numbers whose product is $-10$ and whose sum is $-3$. The numbers $2$ and $-5$ meet these criteria because: $$2\times(-5)=-10\;\text{and}\;2+(-5)=-3$$When we insert these numbers into the blanks, we arrive at the factors: $(n+2)(n-5)$.
