Question

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

Answer 1

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

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