Question
Factorise the expressions and divide them as directed:
$\left(x^2-22 x+117\right) \div(x-13)$
$\left(x^2-22 x+117\right) \div(x-13)$
✓
Answer
$\left(x^2-22 x+117\right) \div(x-13)$
$=\frac{\text{x}^2-22\text{x}+117}{\text{x}-13}$
$=\frac{\text{x}^2-13\text{x}-9\text{x}+117}{\text{x}-13}$
$=\frac{\text{x}(\text{x}-13)-9(\text{x}-13)}{\text{x}-13}$
$=\frac{(\text{x}-13)(\text{x}-9)}{\text{x}-13}$
$=\text{x}-9$
$=\frac{\text{x}^2-22\text{x}+117}{\text{x}-13}$
$=\frac{\text{x}^2-13\text{x}-9\text{x}+117}{\text{x}-13}$
$=\frac{\text{x}(\text{x}-13)-9(\text{x}-13)}{\text{x}-13}$
$=\frac{(\text{x}-13)(\text{x}-9)}{\text{x}-13}$
$=\text{x}-9$
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