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Question

The factors of x4+x2+25 are


A

(x2+3x+5)(x23x+5)

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B

(x2+3x+5)(x2+3x5)

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C

(x2+x+5)(x2x+)

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D

None of these

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Solution

The correct option is A

(x2+3x+5)(x23x+5)


x4+x2+25=x4+25+x2=(x2)2+(5)2+2×x2×59x2=(x2+5)2(3x)2=(x2+5+3x)(x2+53x)=(x2+3x+5)(x23x+5)


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