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Let p(x) be a polynomial such that when divided by (x−1) it leaves the remainder 2 and when divided by (x − 2) it leaves the remainder 1. What is the remainder when it is divided by (x − 1)(x − 2)?

Mathematics
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when we divide by a second degree polynomial the remainder will generally be linear.so the division statement becomes\[P(x)=(x-1)(x-2)q(x)+ax+b\]does that help?
u just need to evaluate \(a\) and \(b\) regarding given conditions for problem
using the remainder thrm P(1) = 2 ; and P(2) = 1 P(x) = -x+3 is my idea

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Other answers:

@mukushla can we write like that ? a and b do not change in both eqns ?
what do u mean by both equations?
using p(1) and p(2),we get 2 eqns.. well is it the ggeneralised form? how?
I think that will give remainder in terms of x
hmm,,remainder shouldn't be some numerical ?
when we divide by a linear polynomial the remainder will be a number. when we divide by a second degree polynomial the remainder will be a linear poly. and ...
ahh i see...yep..got it..
so we have p(1) = 2 = a + b and p(2) = 1 = 2a + b is that right ?
yes thats right.
so rem is -x + 3 ! ahh..thank you sir..
np :)

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