Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 132

Find the positive integer values of $k$ for which the polynomial $y^2 + 5y + k$ are factorable over the integers



$
\begin{array}{c|c}
\text{Factors whose sum is 5} & k \\
\hline\\
1,4 & 4 \\
2,3 & 6
\end{array}
$

The positive integer values of $k$ are $4$ and $6$. So the polynomials are $y^2+5y+4$ and $y^2+5y+6$.