Question
Divide: $44(x^4– 5x^3– 24x^2)$ by $11x(x – 8)$
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Answer
Factorising $44(x^4– 5x^3– 24x^2)$, we get
$44(x^4– 5x^3– 24x^2)$
$= 2 \times 2 \times 11 \times x^2(x^2- 5x - 24)$ [taking the common factor $x^2$ out of the bracket]
$= 2 \times 2 \times 11 \times x^2(x^2– 8x + 3x – 24)$
$= 2 \times 2 \times 11 \times x^2[x(x – 8) + 3(x – 8)]$
$= 2 \times 2 \times 11 \times x^2 \times (x + 3)(x – 8)$
Therefore, $4(x^4– 5x^3– 24x^2) \div 11x(x - 8)$
$= \frac{2 \times 2 \times 11 \times x \times x \times(x+3) \times(x-8)}{11 \times x \times(x-8)}$
$= 2 \times 2 \times x(x + 3) = 4x(x + 3)$
$44(x^4– 5x^3– 24x^2)$
$= 2 \times 2 \times 11 \times x^2(x^2- 5x - 24)$ [taking the common factor $x^2$ out of the bracket]
$= 2 \times 2 \times 11 \times x^2(x^2– 8x + 3x – 24)$
$= 2 \times 2 \times 11 \times x^2[x(x – 8) + 3(x – 8)]$
$= 2 \times 2 \times 11 \times x^2 \times (x + 3)(x – 8)$
Therefore, $4(x^4– 5x^3– 24x^2) \div 11x(x - 8)$
$= \frac{2 \times 2 \times 11 \times x \times x \times(x+3) \times(x-8)}{11 \times x \times(x-8)}$
$= 2 \times 2 \times x(x + 3) = 4x(x + 3)$
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