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hw7 - (1(a Let f(x g(x be polynomials with real...

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(1) (a) Let f ( x ) , g ( x ) be polynomials with real coefficients. Prove that there exists a unique polynomial h ( x ) = x k + a k - 1 x k - 1 + . . . + a 0 such that h ( x ) divides both f ( x ) and g ( x ) and every other polynomial that divides both f ( x ) and g ( x ) divides h ( x ). h ( x ) is called the greatest common divisor of f ( x ) and g ( x ) and is denoted by ( f ( x ) , g ( x )). Hint: Use Euclidean algorithm to construct
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