Answer
$(g-7)(g+2)$
Work Step by Step
To factor a trinomial in the form $g^2+bg+c$, 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 $(g+\_)(g+\_)$.
In the case of $g^2-5g-14$, we are looking for two numbers whose product is $-14$ and whose sum is $-5$. The numbers $-7$ and $2$ meet these criteria because: $$-7\times(2)=-14\;\text{and}\;-7+(2)=-5$$When we insert these numbers into the blanks, we arrive at the factors: $(g-7)(g+2)$.
