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

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

y + 11 = (1/4)(x + 16)

step-by-step explanation: