Answer
$(x+19)(x+2)$
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 $x^2+21x+38$, we are looking for two numbers whose product is $38$ and whose sum is $21$. The numbers $19$ and $2$ meet these criteria because: $$19\times(2)=38\;\text{and}\;19+(2)=21$$When we insert these numbers into the blanks, we arrive at the factors: $(x+19)(x+2)$.
