Factorise:

The given expression is $x^{2}-22 x+117$.

Find two numbers that follow the conditions given below:

Sum $=-22$

Product $=117$

Clearly, the numbers are $-13$ and $-9$.

$x^{2}-22 x+117=x^{2}-13 x-9 x+117$

$=x(x-13)-9(x-13)$

$=(x-13)(x-9)$