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shubhamsrg
 3 years ago
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)?
shubhamsrg
 3 years ago
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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mukushla
 3 years ago
Best ResponseYou've already chosen the best response.4when we divide by a second degree polynomial the remainder will generally be linear.so the division statement becomes\[P(x)=(x1)(x2)q(x)+ax+b\]does that help?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.4u just need to evaluate \(a\) and \(b\) regarding given conditions for problem

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0using the remainder thrm P(1) = 2 ; and P(2) = 1 P(x) = x+3 is my idea

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0@mukushla can we write like that ? a and b do not change in both eqns ?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.4what do u mean by both equations?

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0using p(1) and p(2),we get 2 eqns.. well is it the ggeneralised form? how?

sauravshakya
 3 years ago
Best ResponseYou've already chosen the best response.1I think that will give remainder in terms of x

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0hmm,,remainder shouldn't be some numerical ?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.4when 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
 3 years ago
Best ResponseYou've already chosen the best response.0ahh i see...yep..got it..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0so we have p(1) = 2 = a + b and p(2) = 1 = 2a + b is that right ?

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0so rem is x + 3 ! ahh..thank you sir..
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