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Yes.
Usually the sum will have the same degree as the highest degree of the polynomials that are added. However, it is also possible for the highest term to cancel, for example if one polynomial has an x3, and the other a -x3. In this case, the sum will have a lower degree.
The question cannot be answered because the ratio of the polynomials cannot simplify to "3x-12x plus 1" since that is not a simplified form: it simplifies to -9x + 1.
Descartes did not invent polynomials.
dividing polynomials is just like dividing whole nos..