Polynomial help

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). THANKS...PLEASE ANSWER THIS

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 $R(x)$ ?

Jimmy Kariznov - 7 years, 9 months ago

So what is missing in this question? Actually, the question is correct and needs no more given quantity.. Thanks

Kumar Ashutosh - 7 years, 9 months ago

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.

Bob Krueger - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$