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Question

Factorize x6+27 _______________.

A
(x2+3)(x2+3x+3)(x23x+3)
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B
(x23)(x2+3x+3)(x2+3x+3)
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C
(x2+3)(x44x2+9)2
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D
(x2+3)(x23x+3)(x23x3)
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Solution

The correct option is C (x2+3)(x44x2+9)2
x6+27=(x2)3+33

This is of the form a3+b3=(a+b)(a2ab+b2).

Therefore,
(x2)3+33=(x2+3)(x43x2+9)

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