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a + b=? remainder P(x):(x^3 + ax + b)=remainder P(x):(x^3 + ax^2 + b)

Source: Flanders Math Olympiad 2014 p4

December 24, 2022
algebrapolynomial

Problem Statement

Let P(x)P(x) be a polynomial of degree 55 and suppose that a and b are real numbers different from zero. Suppose the remainder when P(x)P(x) is divided by x3+ax+bx^3 + ax + b equals the remainder when P(x)P(x) is divided by x3+ax2+bx^3 + ax^2 + b. Then determine a+ba + b.
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