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2015-04-19T09:47:40+05:30

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In view of expressing the given expression as difference of perfect squares, split x^2 as 10x^2-9x^2 :

x^4+x^2+25~=~x^4+10x^2-9x^2+25\\=x^4+10x^2+25-9x^2\\=(x^2+5)^2-(3x)^2\\=(x^2+5+3x)(x^2+5-3x)\\=(x^2+3x+5)(x^2-3x+5)
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2015-04-19T11:03:21+05:30

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first you need to split the middle term.

= x^{4} +10 x^{2} -9 x^{2} +25

= x^{4}+10 x^{2} +25-9 x^{2}

= ( x^{2}+5 )^{2} -  (3x)^{2}     ( (a^{2} - b^{2} = (a+b)(a-b) )

=( x^{2} +5+3x) ( x^{2} +5-3x)

The factors are : ( x^{2} +3x+5)( x^{2} -3x+5)
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