Consider the polynomials
(ab2+ 3ab+ 8a2) (-5ab2)
use the polynomials to illustrate the following:
a. polynomials are closed under addition
b. polynomials are closed under subtraction
c. polynomials are closed under multiplication
d. polynomials are not closed under division

Hello from MrBillDoesMath!

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

what's that

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.