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 .