1.

Factorize: x4 + x2 + 25

Answer»

x4 + x2 + 25 

= (x2)2 + 52 + x2     [a2 + b2 = (a + b)2 – 2ab]

= (x2 + 5)2 −2(x2) (5) + x2 

= (x2 + 5) 2 −10x2 + x2 

= (x2 + 5)2 − 9x2 

= (x2 + 5)2 − (3x)2    [a2 – b2 = (a + b)(a – b ] 

= (x2 + 3x + 5)(x2 − 3x + 5)


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