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Abstract Algebra! if you could explain the steps it would be helpful!

7. Let ri,r2,..., Tn be distinct integers. The goal of this problem is to prove that the polynomial p(z)- (a) Suppose that p(x)-f(x)g(x) for polynomials f and g in Zfx] with 1 deg(f), deg(g) S n-1. Prove (b) With notation as in part (a), deduce that f(x) +g(x) has at least n distinct roots and must therefore (z-T1) (x-r2) . . . (x-rn)-1 İs always irreducible in Q[2] that f(ri)--g(ri) for each 1 < i <n be the zero polynomial. Show that f(x)g(x)cannot yield a valid factorization, and conclude that px) is irreducible.

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