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Question

Factorize : x4+x2+25.

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Solution

x4+x2+25(x2)2+(5)2+2x2×52x2×5+x2(x2)2+(5)2+10x210x2+x2=(x2)2+(5)2+10x29x2=(x2+5)2(3x)2{a2b2=(a+b)(ab)}=(x2+53x)(x2+5+3x)=(x23x+5)(x2+3x+5)


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