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Advanced MathHardCounting real linear factors

Advanced Math practice question

When x⁴ − 16 is factored completely over the real numbers, how many distinct linear factors appear?

  1. A. 2Correct
  2. B. 4
  3. C. 1
  4. D. 0

Answer: A. 2

x⁴ − 16 = (x² + 4)(x² − 4) = (x² + 4)(x − 2)(x + 2). The quadratic x² + 4 has no real roots, leaving two linear factors.

Why the other answers are wrong

B. 4
Four would require x² + 4 to split further, but it has no real roots.
C. 1
Both (x − 2) and (x + 2) appear — two distinct linear factors.
D. 0
x² − 4 does factor into linear pieces: (x − 2)(x + 2).

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