Factorise:

The given expression is $x^{2}-23 x+42$.

Find two numbers that follow the conditions given below:

Sum $=-23$

Product $=42$

Clearly, the numbers are $-21$ and $-2$.

$x^{2}-23 x+42=x^{2}-21 x-2 x+42$

$=x(x-21)-2(x-21)$

$=(x-21)(x-2)$