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When a polynomial f(x) is divided by x² - 3x + 2, the remainder is a*x + b. Given f(1) = 4 and f(2) = 7, find the values of a and b.

1. a = 3, b = 1
2. a = 1, b = 3
3. a = 2, b = 2
4. a = 4, b = 0

Correct answer: a = 3, b = 1

Solution

Since the divisor factors as (x-1)(x-2), substituting its roots makes the quotient term vanish, leaving the linear remainder equal to f at those points.

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