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Given that a² + b² + c² = -2 and f(x) = |[1+a²x, (1+b²)x, (1+c²)x; (1+a²)x, 1+b²x, (1+c²)x; (1+a²)x, (1+b²)x, 1+c²x] |, what is the degree of the polynomial f(x)?

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

Correct answer: 2

Solution

Doing R1->R1-R2 and R2->R2-R3 factors out (1-x)^2, and the remaining 3x3 expands to 1+(2+a^2+b^2+c^2)x = 1 (since a^2+b^2+c^2=-2). So f(x)=(1-x)^2, degree 2.

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