The correct option is C ( x+3 ) ( x 3 ) ( x^2+9 ) x^4 81= ( x^2 )^2 ( 9 )^2= ( x^2+9 ) ( x^2 9 ) = #160; ( x^2+9 ) ( x 3 ) ( x+3 ) ...

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Logarithmic Differentiation

x4-81=

Question

$x^{4} - 81$ =______

(x^{2} + 81) (x^{2} - 1)

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(x^{2} - 9) (x^{2} - 9)

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(x + 3) (x - 3) (x^{2} + 9)

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(x^{2} - 9) (x + 3)

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Solution

The correct option is C $(x + 3) (x - 3) (x^{2} + 9)$
$x^{4} - 81 = {(x^{2})}^{2} - {(9)}^{2} = (x^{2} + 9) (x^{2} - 9)$
= $(x^{2} + 9) (x - 3) (x + 3)$

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Divide $(x^{2} + 3) (x^{2} - 3) + 9$ by $x^{4}$ [1 MARK]

Dividing $(x^{2}) + 3) (x^{2} - 3) + 9$ by $x^{4}$ gives

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