Answer
$(t-15)(t+2)$
Work Step by Step
To factor a trinomial in the form $t^2+bt+c$, 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 $(t+\_)(t+\_)$.
In the case of $t^2-13t-30$, we are looking for two numbers whose product is $-30$ and whose sum is $-13$. The numbers $-15$ and $2$ meet these criteria because: $$-15\times(2)=-30\;\text{and}\;-15+(2)=-13$$When we insert these numbers into the blanks, we arrive at the factors: $(t-15)(t+2)$.
