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If the polynomial a4*x⁴ + a3*x³ + a2*x² + a1*x + a0 equals the determinant | x²+x, x-2, 1 | | 2x+3, x, 3 | | x-5, -1, x+1| as an identity in x, then the value of (a4 + a3 + a2 + a1 + a0) - 25 is:

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

Correct answer: 2

Solution

Setting x=1 gives the sum a4+a3+a2+a1+a0 = det at x=1 = 27, so 27-25 = 2.

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