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Rationalisation

Divide: q2-4...

Question

Divide: $q^{2} - 4 q - 32$ by $q + 4$

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Solution

given, $q^{2} - 4 q - 32 \div q + 4$

$= \frac{q^{2} - 4 q - 32}{q + 4}$

$= \frac{q^{2} - 8 q + 4 q - 32}{q + 4}$

$= \frac{q (q - 8) + 4 (q - 8)}{q + 4}$

$= \frac{(q - 8) (q + 4)}{q + 4}$

$= q - 8$

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