Given,

x² – 22x + 117

Now, first we have to find out the numbers whose-

Sum = - 22 and

Product = 117

The numbers are 13 and 9,

So,

x² – 22x + 117 = x² – 13x – 9x + 117

= x(x – 13) – 9(x – 13)

= (x – 13)(x – 9)