Factorise:

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 $-9$.

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

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

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

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