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When a polynomial f(x) is divided by (x² - 5x + 6), the remainder is (ax + b). Given f(2) = 5 and f(3) = 8, find (a, b).
- (3, 1)
- (2, -1)
- (3, -1)
- (3, -2)
Correct answer: (3, -1)
Solution
f(x) = (x-2)(x-3)*Q(x) + ax + b. At x=2: 2a+b=5. At x=3: 3a+b=8. Subtracting: a=3, b=-1.
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