We need two numbers that multiply to $-156$ and add to $-1$ (the coefficient of $x$).

Test factor pairs of $-156$:

$(-13)(12) = -156 \quad \text{and} \quad -13 + 12 = -1 \; \checkmark$

So:

$x^2 - x - 156 = (x - 13)(x + 12)$

The binomial $x - 13$ is a factor.