Let P(x) be a nonconstant complex coefficient polynomial and let Q(x,y)=P(x)−P(y). Suppose that polynomial Q(x,y) has exactly k linear factors unproportional two by tow (without counting repetitons). Let R(x,y) be factor of Q(x,y) of degree strictly smaller than k. Prove that R(x,y) is a product of linear polynomials.Note: The degree of nontrivial polynomial ∑m∑ncm,nxmyn is the maximum of m+n along all nonzero coefficients cm,n. Two polynomials are proportional if one of them is the other times a complex constant.Proposed by Navid Safaie polynomialalgebracontest problemmultivariate polynomial