Yes. Note that specifically, the sum might be a constant (just a number), or even zero, but it is convenient to include those in the definition of "polynomial".
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The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
No. Even if the answer is zero, zero is still a polynomial.
Clouser
Closure
That property is called CLOSURE.