When a polynomial P(x) is divided by x-1, the remainder is 2. When P(x) is divided by x-2, the remainder is 1. Find the Remainder when P(x) is divided by (x-1)(x-2).
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4 years, 1 month ago
You know that \(P(x) = (x-1)Q_1(x)+2\) and \(P(x) = (x-2)Q_2(x)+1\) for some polynomials \(Q_1(x)\) and \(Q_2(x)\). What is \(P(1)\)? What is \(P(2)\)?
Then, write \(P(x) = (x-1)(x-2)Q(x)+R(x)\) where \(Q(x)\) is a polynomial and \(R(x)\) is a linear polynomial. What is \(R(1)\)? What is \(R(2)\)? Now, what is \(R(x)\)?
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So what is missing in this question?
Actually, the question is correct and needs no more given quantity..
Jimmy doesn't think there is anything wrong with the problem. He is just showing you the thought processes to reach the answer, without actually telling you the answer. If you follow what he is showing, it is not hard, at least at your level, to find the answer.