By factorising x2 - 22x + 117, evaluate:
(x2 - 22x + 117) ÷ (x - 13).
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(x2 - 22x + 117) ÷ (x - 13)
= (x2 - 13x - 9x + 117) ÷ (x - 13)
= [x(x - 13) - 9(x - 13)] ÷ (x - 13)
= (x - 13)(x - 9) ÷ (x - 13)
= (x - 9)
Hence, (x2 - 22x + 117) ÷ (x - 13) = (x - 9).
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