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1. Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.
2. Explain why the degree of the sum of two polynomials of different degrees equals the larger of their degrees.
3. Give a careful statement about the degree of the sum of two polynomials of the same degree.
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1. Because leading terms multiply, deg (??) = ? + ?.
2. The larger degree predominates when there are several degrees.
3. The sum is often that degree when the leading terms cancel, although it can drop.
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