Factorize $a^2-ab-bc\pm c^2$ I got this question in a test but it did not specify the variable with respect to which I was supposed to factorize
$$a^2-ab-bc\pm c^2$$
where it could be just $a(a-b)-c(b\pm c)$ but no common factor over all terms. I feel I may be missing something. The $\pm$ is there because I cannot remember whether the last sign was minus or plus.
Is there some trick to factorize this or is this question vacuous? What does it mean to factorize this?

We observe that
\begin{eqnarray}
a^2-ab-bc+c^2&=&a^2+c^2-b(a+c)\\
&=&(a+c)^2-b(a+c)-2ac\\
&=&(a+c)^2-b(a+c)+\frac{b^2}{4}-\frac{b^2+8ac}{4}\\
&=&\left(a+c-\frac{b}{2}\right)^2-\frac{b^2+8ac}{4}.
\end{eqnarray}
Hence, if $b^2+8ac\geq 0$ then
$$
a^2-ab-bc+c^2=\left(a+c-\frac{b}{2}+\sqrt{\frac{b^2+8ac}{4}}\right)\left(a+c-\frac{b}{2}-\sqrt{\frac{b^2+8ac}{4}}\right)
$$
