Divide $44 (x^{4} - 5 x^{3} - 24 x^{2})$ by $11 x (x - 8)$ . [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

$44 (x^{4} - 5 x^{3} - 24 x^{2})$

$= 2 \times 2 \times 11 \times x^{2} (x^{2} - 5 x - 24)$

$= 2 \times 2 \times 11 \times x^{2} (x^{2} - 8 x + 3 x - 24)$

$= 2 \times 2 \times 11 \times x^{2} {x (x - 8) + 3 (x - 8)}$

$= 2 \times 2 \times 11 \times x^{2} (x + 3) (x - 8)$

Therefore,
$44 (x^{4} - 5 x^{3} - 24 x^{2}) \div 11 x (x - 8)$ .

$= \frac{2 \times 2 \times 11 \times x \times x \times (x + 3) \times (x - 8)}{11 \times x \times (x - 8)}$

$= 2 \times 2 \times x (x + 3)$

$= 4 x (x + 3)$

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