Given 2 distinct remainders, find remainder when Polynomial is divided by product of the factors

Описание к видео Given 2 distinct remainders, find remainder when Polynomial is divided by product of the factors

Credit to Xu Jiagu for sharing this problem type in his Math Olympiad Lecture Notes
If a polynomial P(x) has remainders 7 and 13 when divided by
(x-3) and (x- 4) respectively, find the remainder when
P(x) is divided by (x-3)(x- 4)
More abstractly/generally, a Polynomial has 2 distinct constant remainders when divided by two distinct linear factors. Find the remainder when the same polynomial is divided by the product of the two linear factors.
The remainder theorem, division algorithm and degree considerations were all useful notions solving this problem.
Read outstanding June 2015 mathematician Andrew D. Hwang coverage of this topic.

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