The factors of ( $x^{4} - 625)$ are

(– 25), ( + 25)

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( + 25)

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( - 10x + 25), ( + 5x + 25)

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Do not exist.

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Solution

The correct option is A: $(x^{2} - 25), (x^{2} + 25)$
( $x^{4} - 625)$
$= (x^{2})^{2} - (25)^{2}$
$= (x^{2} - 25) (x^{2} + 25)$ [ $∵ (a^{2} + b^{2}) = (a + b) (a - b)$ ]
Factors of ( $x^{4}$ + 625) are $(x^{2} - 25), (x^{2} + 25)$

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