CTET Feb16p2, q55
0. One of the factors of x4 + 4 is
- Option : C
- Explanation : x4 + 4 = (x2)2 + (2)2
= (x2 + 2)2 - 2.(x2).(2) [As a2 + b2 = (a+b)2 - 2ab]
= (x2 + 2)2 - 4x2
= (x2 + 2)2 - (2x)2
= (x2 + 2 + 2x)(x2 + 2 - 2x) [As a2 - b2 = (a+b)(a-b)]
∴ (x2 - 2x + 2) is a factor of x4 + 4.
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