Advanced Math practice question

Answer: A. (x² + 4)(x − 2)(x + 2)

x⁴ − 16 is a difference of squares: (x²)² − 4² = (x² − 4)(x² + 4). The first factor is itself a difference of squares, (x − 2)(x + 2). The second, x² + 4, doesn't factor further over the real numbers.

Why the other answers are wrong

B. (x² − 4)²

(x² − 4)² is x⁴ − 8x² + 16 — a plus 16 and a middle term. A difference of squares never factors as a perfect square.

C. (x − 2)²(x + 2)²

(x − 2)²(x + 2)² equals (x² − 4)², which is x⁴ − 8x² + 16, not x⁴ − 16.

D. (x² + 4)²

(x² + 4)² expands to x⁴ + 8x² + 16.

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