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Solving a Quadratic Equation by Completion of Squares Method

Divide x2-2...

Question

Divide $x^{2} - 23 x^{2} + 142 x - 120$ by $(x - 1)$ by long division method.

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Solution

$x - 1) x^{3} - 23 x^{2} + 142 x - 120 (x^{2}$
$x^{3} - x^{2}$
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$x - 1) - 22 x^{2} + 142 x - 120 x (- 22 x$
$- 22 x^{2} + 22 x$
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$x - 1) 120 x - 120 (120$
$120 x - 120$
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$0$
$x^{3} - 23 x^{2} + 142 x - 120 = (x - 1) (x^{2} - 22 x + 120)$

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