Good evening and thank you very much. Question about polynomial closure.

Question

 

I am trying to explain to someone why polynomials are closed under addition, subtraction and multiplication. I was going to tell them that even though in some cases these operations can produce a zero, they do not contradict the definition of closure, since zero itself is a type of polynomial where all the coefficients are zeroes. Please let me know if this is an accurate answer. Thank you

Answer 1

That answer is accurate.