Thread: Remainder of a polynomial

If p(x) is a polynomial, which when divided (x-1) gives a remainder of 2 and when divided by (x-2) gives a remainder of 1. What is the remainder when it is divided by (x-1)(x-2)?
I have been able to get answers for a few polynomials(eg. -(x^2)/3 + 7/3) that give those remainders, but how do you solve it in general?

Originally Posted by nahduma

If p(x) is a polynomial, which when divided (x-1) gives a remainder of 2 and when divided by (x-2) gives a remainder of 1. What is the remainder when it is divided by (x-1)(x-2)?
I have been able to get answers for a few polynomials(eg. -(x^2)/3 + 7/3) that give those remainders, but how do you solve it in general?

Have you tried writing as p(x) = q(x)g(x) + r(x)?

Edit: Actually I'm not sure if the above is helpful, but maybe an approach that will work is an extension of the Chinese remainder theorem.

Edit 2 (written LONG after the original post and first edit): Since my answer wasn't very elucidating, I'm posting links to two other threads, here and here, which give better answers than what I gave.