The basic polynomial operations include the following operations:
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Finding the order of a polynomial
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Evaluating a polynomial
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Adding, subtracting, multiplying, or dividing polynomials
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Determining the composition of a polynomial
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Determining the greatest common divisor of two polynomials
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Determining the least common multiple of two polynomials
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Calculating the derivative of a polynomial
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Integrating a polynomial
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Finding the number of real roots of a real polynomial