Question

a. Think of polynomials as a system. For each of the following operations, determine whether the system is closed under the operation. In each case, explain why it is closed or provide an example showing that it isn’t.

1. Addition

Answer 1

HI!!

Answer 2

Hi

Answer 3

make up two polynomials any polynomials

Answer 4

then add them, which is the same thing as "combine like terms"
the result will also be a polynomial
that means they are "closed under addition"

Answer 5

(21+48x)*(36+12x)

Answer 6

it says "addition" right? not multiplication

Answer 7

oh good point

Answer 8

so you could have maybe
\[(21+48x)+(36+12x)\] as an addition using your example

Answer 9

okay

Answer 10

when you add you get another polynomial, namely
\[57+50x\]

Answer 11

you also get another polynomial when you multiply

Answer 12

and when you subtract

Answer 13

but NOT when you divide