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Let's try an example:The difference between (6x3 + x2 - 4x + 9) and (6x3 + x2 - 4x + 7) is 2 .2 is a polynomial of degree 0, so this example would appear to support the hypothesis in the question.However, polynomials cannot include negative exponents. So, (2x)/(2x2) produces 1/x, which is not a polynomial.So no, not always.
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Adding and subtracting polynomials is simply the adding and subtracting of their like terms.
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
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