Answer
$k^2+5k+6=(k+2)(k+3)$
Work Step by Step
We are trying to fill in the blank in the equation $k^2+5k+6=(k+2)(k+\square)$. In order to do so, we will factor the trinomial on the left side of the equation to determine the second factor.
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 $k^2+5k+6$, we are looking for two numbers whose product is $6$ and whose sum is $5$. The numbers $2$ and $3$ meet these criteria, because $$2\times(3)=6\;\text{and}\;2+(3)=5$$When we insert these numbers into the blanks, we arrive at the factors $(k+2)(k+3)$.
Inserting factored form back into the original equation, we have the complete equation, which is $k^2+5k+6=(k+2)(k+3)$.
