Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 126

Determine all integers $k$ such that the trinomial $x^2 - kx + 14$ can be factored over the integers

The factors must have the same sign

$\begin{array}{c|c}
\text{Factor of 14} & \text{Sum } (k) \\
\hline \\
-1,-14 & -15 \\
-2,-7 & -9
\end{array} $

The values of $k$ that the trinomial can be factored over the integers are $-9$ and $-15$.