Question

How do I tell if polynomials are closed under addition and subtraction?

Answer 1

\[\sum a_nx^n + \sum b_nx^n\]

look familiar?

Answer 2

Yeah. So how do I use that to figure out what its closed under

Answer 3

the sums can be put together,
\[\sum (a_n + b_n)x^n\]

Answer 4

The sums of the Polynomials, right?

Answer 5

right. Each sum is a polynomial. When you add polynomials, you "combine like terms" by adding the coefficients:

ex: (2x+3) + (5x-7) = (2+5)x + (3-7) = another polynomial

Answer 6

Ok. So I use the equation you showed?

Answer 7

Have you used the summation notation before, either in class or on another problem?

Answer 8

Tbh no i have not

Answer 9

right... so don't use that .... :)

Answer 10

How formal does your answer need to be?

Answer 11

This is what my question said: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer

Answer 12

Sounds like you just need to provide a sentence or two, maybe based on what you got in the previous parts.

BTW, polynomials are in fact closed under addition, subtraction, and multiplication.

The fact is, when you add or subtract polynomials you simply "combine like terms" by adding or subtracting the coefficients of variable terms of the same degree.

Then you can use what you got in part A and B as an example.

Answer 13

the word "closed" here means that when you add/subtract polynomials you get another polynomial as the result

Answer 14

so it means if i add, subtract or multiply, I get another polynomial?

Answer 15

If you start with polynomials, ... yep ...

Answer 16

oh. sounds more complicated though

Answer 17

Is this for a class? If so, which one?

Answer 18

Algebra 1

Answer 19

The answer to this question can get very complicated, technically. This is a question that can be posed in sophomore and higher classes in pure mathematics in college, and the answers can span several pages :)

For Algebra I I think they just want to get you to see that when you are working with polynomials, things are kinda nice and predictable.

Answer 20

I think they think I am the Chosen One O.O

Answer 21

Awesome! (How do you know your not :)

Answer 22

I WILL BRING BALANCE TO THE FORCE!

Answer 23

well thanks for the help!

Answer 24

Np, had fun.

Answer 25

You too. Bye!