Question: Factorise:
x2 − 22x + 117
Solution:
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 $-9$.
$x^{2}-22 x+117=x^{2}-13 x-9 x+117$
$=x(x-13)-9(x-13)$
$=(x-13)(x-9)$
