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Iran polynomial

Source: Iranian TST 2019, third exam day 1, problem 1

April 15, 2019
algebrapolynomial

Problem Statement

Find all polynomials P(x,y)P(x,y) with real coefficients such that for all real numbers x,yx,y and zz: P(x,2yz)+P(y,2zx)+P(z,2xy)=P(x+y+z,xy+yz+zx).P(x,2yz)+P(y,2zx)+P(z,2xy)=P(x+y+z,xy+yz+zx).
Proposed by Sina Saleh
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