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MATHMAA

Irreducible Polynomial Theorem

Proofs of Irreducible Polynomial Theorem :

Theorem 1 : If f , g are two non-zero polynomials over a ring R then

(a) deg(f+g) $$\leq$$ max { deg f, deg g} if f+g $$\neq$$ 0,

(b) deg fg $$\leq$$ deg f + deg g, if fg $$\neq$$ 0

Proof:

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