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?
- A. 2Correct
- B. 4
- C. 1
- 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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