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- shubhamsrg

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)?

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- shubhamsrg

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- anonymous

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?

- anonymous

u just need to evaluate \(a\) and \(b\) regarding given conditions for problem

- amistre64

using the remainder thrm
P(1) = 2 ; and P(2) = 1
P(x) = -x+3
is my idea

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- shubhamsrg

@mukushla can we write like that ? a and b do not change in both eqns ?

- anonymous

what do u mean by both equations?

- shubhamsrg

using p(1) and p(2),we get 2 eqns..
well is it the ggeneralised form? how?

- anonymous

I think that will give remainder in terms of x

- shubhamsrg

hmm,,remainder shouldn't be some numerical ?

- anonymous

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 ...

- shubhamsrg

ahh i see...yep..got it..

- shubhamsrg

so we have
p(1) = 2 = a + b
and
p(2) = 1 = 2a + b
is that right ?

- anonymous

yes thats right.

- shubhamsrg

so rem is -x + 3 !
ahh..thank you sir..

- anonymous

np :)

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