If polynomial f(x) leaves remainder 3 when divided by (x - 2) and leaves remainder 5 when divided by (x - 3), what is th...
Type: MCQ • Marks: 1
If polynomial f(x) leaves remainder 3 when divided by (x - 2) and leaves remainder 5 when divided by (x - 3), what is the remainder when f(x) is divided by (x - 2)(x - 3)?
Options
A. 2x - 1
B. 5x - 3
C. x + 1
D. 3x - 1
Explanation
Let remainder be ax + b. f(2) = 2a + b = 3 and f(3) = 3a + b = 5. Solving gives a = 2, b = -1, so remainder is 2x - 1.
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