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The expression x4 + 7x2 + 16 can be factored as :
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- (2 + x + 1) (2 + x + 16)
- (2 + x + 1) (2 − x + 16)
- (2 + x + 4) (2 − x + 4)
- (2 + x − 4) (2 − x − 4)
Correct Option: C
The given expression x4 + 7x2 + 16 = ( x4 + 8x2 + 16 ) - x2
= ( x4 + 2 * 4 * x2 + 42 ) - x2
= ( x2 + 4 )2 - x2
= ( x2 + 4 + x ) ( x2 + 4 - x )
Hence , x4 + 7x2 + 16 = ( x2 + x + 4 ) ( x2 - x + 4 ).
Option C is correct answer .
