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Given a² + b² + c² = -2 and f(x) is the 3x3 determinant | 1 + a²*x (1 + b²)*x (1 + c²)*x | | (1 + a²)*x 1 + b²*x (1 + c²)*x | | (1 + a²)*x (1 + b²)*x 1 + c²*x | then f(x) is a polynomial of degree:

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

Carrying out the standard simplification, the highest surviving power of x is 1 (the leading x²/x³ contributions cancel using a²+b²+c² = -2), so f(x) is a degree-1 polynomial.

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