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Yes. If the coefficient of the third degree terms in one polynomial are the additive inverses (minus numbers) of the coefficient of the corresponding terms in the second polynomial.

Eg:

3x3 + 2x2 + 5

and

-3x3 + x - 7

add to give 2x2 + x - 2

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Q: Can two third-degree polynomials be added to produce a second-degree polynomial?
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