A polynomial \(P(x)\) leaves a remainder \(2\) when divided by \((x - 1)\) and a remainder \(1\) when divided by \((x - 2)\). The remainder when \(P(x)\) is divided by \((x - 1)(x - 2)\) is
Question and options
A polynomial leaves a remainder when divided by and a remainder when divided by . The remainder when is divided by is
Answer and explanation
Correct answer: A - \(3-x\)
Remainder ax+b with P(1)=a+b=2 and P(2)=2a+b=1 gives a=-1, b=3: remainder 3-x.
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