MathDB

3

Part of 1990 ITAMO

Problems(1)

P(x) upon division by (x-a)(x-b)(x-c) when P(a)=a, P(b)=b, P(c)=c

Source: 1990 ITAMO p3

1/31/2020
Let a,b,ca,b,c be distinct real numbers and P(x)P(x) a polynomial with real coefficients. Suppose that the remainders of P(x)P(x) upon division by (x−a),(x−b)(x-a), (x-b) and (x−c)(x-c) are a,ba,b and cc, respectively. Find the polynomial that is obtained as the remainder of P(x)P(x) upon division by (x−a)(x−b)(x−c)(x-a)(x-b)(x-c).
polynomialremainderalgebra