Hello from MrBillDoesMath!
Answer:
See Discussion for details
Discussion:
Polynomials are closed with respect to an operation if applying that operation to them generates another polynomial
A. ( ab^2 + 3ab + 8a^2) + ( - 5ab^2) =
-4ab^2 + 3ab + 8a^2 which is a polynomial
B. ( ab^2 + 3ab + 8a^2) - ( - 5ab^2) =
6ab^2 + 3ab + 8a^2 which is a polynomial
C. ( ab^2 + 3ab + 8a^2) * ( - 5ab^2) =
-5a^2b^4 - 15a^2b^3 = 40a^3b^2 which is a polynomial
D ( ab^2 + 3ab + 8a^2) / ( - 5ab^2) =
-(1/5) + 3(-1/5) (1/b) + 8 ( -1/5)a(1/b^2)
which is NOT a polynomial because of the (1/b), ( 1/b^2) terms
Thank you,
MrB
