Divide $5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2$ by $x^{2} - x$ .

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Solution

$x^{2} - x) 5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2 (5 x^{3} + 9 x^{2} + 6 x + 8$
$5 x^{5} - 5 x^{4}$
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$9 x^{4} - 3 x^{3}$
$9 x^{4} - 9 x^{3}$
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$6 x^{3} + 2 x^{2}$
$6 x^{3} - 6 x^{2}$
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$8 x^{2} + 2$
$8 x^{2} - 8 x$
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$8 x + 2$

$\frac{5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2}{x^{2} - x} = 5 x^{3} + 9 x^{2} + 6 x + 8 + (\frac{8 x + 2}{x^{2} - x})$

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