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If the determinant of [[x-4, 2x, 2x], [2x, x-4, 2x], [2x, 2x, x-4]] can be written as (A + B x)(x - A)², find the ordered pair (A, B).
- (-4, 3)
- (-4, 5)
- (4, 5)
- (-4, -5)
Correct answer: (-4, 5)
Solution
The determinant equals (5x - 4)(x + 4)² = (-4 + 5x)(x - (-4))², so A = -4 and B = 5, giving (A, B) = (-4, 5).
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