The expression x4 + 7x2 + 16 can be factored as :

Q: The expression x4 + 7x2 + 16 can be factored as :

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 .

(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 Answer: (2 + x + 4) (2 − x + 4)

Explanation:

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 .

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The expression x4 + 7x2 + 16 can be factored as :

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