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Let f(x) = ax⁶ + bx⁵ + cx⁴ + dx³ + ex² + fx + g, where | x² − 2x + 3 7x + 2 x + 4 | | 2x + 7 x² − x + 2 3x | | 3 2x − 1 x² − 4x + 7 | Then the value of g is:

1. −200
2. 100
3. 112
4. −108

Correct answer: −108

Solution

The constant term g equals f(0), the determinant evaluated at x=0: |3,2,4; 7,2,0; 3,-1,7|. Expanding gives 3(14-0) - 2(49-0) + 4(-7-6) = 42 - 98 - 52 = -108.

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