(1)(a) Letf(x), g(x) be polynomials with real coefficients.Prove that there exists auniquepolynomialh(x) =xk+ak-1xk-1+. . .+a0such thath(x) divides bothf(x) andg(x) and every other polynomial that divides bothf(x) andg(x) dividesh(x).h(x) is called the greatest commondivisor off(x) andg(x) and is denoted by (f(x), g(x)).Hint:Use Euclidean algorithm to construct
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Greatest common divisor, real coefficients, Greatest common divisor of two polynomials