Factorize the expression and divide them as directed: $(x^{2} - 22 x + 117) \div (x - 13)$

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Solution

Step 1: Factorize the expression
$x^{2} - 22 x + 117$
$= x^{2} - (9 + 13) x + 117$
$= x^{2} - 9 x - 13 x + 117$
$= x (x - 9) - 13 (x - 9)$
$= (x - 13) (x - 9)$

Step 2: Perform the division of the given expression:
$\frac{x^{2} - 22 x + 117}{x - 13} = \frac{(x - 13) (x - 9)}{x - 13}$
$= (x - 9)$
$∴ \frac{x^{2} - 22 x + 117}{x - 13} = (x - 9)$

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