Question

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)?

Answer 1

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?

Answer 2

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

Answer 3

using the remainder thrm

P(1) = 2 ; and P(2) = 1

P(x) = -x+3

is my idea

Answer 4

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

Answer 5

what do u mean by both equations?

Answer 6

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

Answer 7

I think that will give remainder in terms of x

Answer 8

hmm,,remainder shouldn't be some numerical ?

Answer 9

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 ...

Answer 10

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

Answer 11

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

Answer 12

yes thats right.

Answer 13

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

Answer 14

np :)