The lengths of two sides of a triangle are shown below:
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle?
Part B: What is the length of the third side of the triangle?
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

- MeowLover17

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- MeowLover17

@welshfella

- Hero

@MeowLover17, What is (8x^2 - 5x - 2) + (7x - x^2 + 3) ?

- MeowLover17

One moment

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## More answers

- Jhannybean

Rearrange your terms to combine like terms with eachother. It makes it easier to evaluate.

- MeowLover17

I got +6x^2+2x+1 @Hero

- MeowLover17

Sorry my computer died

- MeowLover17

@Jhannybean

- MeowLover17

Hello hero i got what i wrote above

- MeowLover17

So would that be the total length of the two sides??

- Hero

You should have gotten 7x^2 + 2x + 1

- MeowLover17

Oh sorry yes i see

- MeowLover17

So hero 7x^2 + 2x + 1 <- This is my answer for part A correct?

- MeowLover17

how would i find the length of the third side?

- Hero

To find the length of the third side subtract the result you got for part A from the perimeter.

- MeowLover17

That's what i was thinking let me do that

- MeowLover17

so i would receive -4x^3+10^2+7?

- MeowLover17

for the length of the third side

- Hero

Subtract this way:
|dw:1441579511663:dw|

- MeowLover17

ok

- MeowLover17

-4x^3 -4x^2-5x-3

- MeowLover17

Is what i got

- MeowLover17

and if thats correct please help me with part C because i dont understand what its asking.

- Hero

What is 4x^3 minus zero?

- Hero

|dw:1441579942249:dw|

- MeowLover17

+4x^3

- MeowLover17

4x^3 -4x^2-5x-3

- Hero

What is -3x^2 -(-x^2) ?

- MeowLover17

-2x^2

- Hero

Yes. When you're subtracting one expression from the other, you have to flip the signs.

- MeowLover17

Oh i understand i forgot to change the signs

- MeowLover17

Yes :/

- MeowLover17

so i get 4x^3-2x^2-5x-9

- MeowLover17

For the third side

- mathstudent55

|dw:1441580340586:dw|

- mathstudent55

|dw:1441580483756:dw|

- mathstudent55

To find the third side, subtract the sum of the lengths of the first two sides (Part A) from the perimeter.

- MeowLover17

Okay so i would recieve 4x^3-10x^2-7

- MeowLover17

Right?

- Hero

Somehow I wrote the second term incorrectly.

- MeowLover17

I just noticed that lol

- MeowLover17

But hero now that i have done gotten part B how do i do part 3?

- MeowLover17

Part B is 4x^3-10x^2-7 correct?

- mathstudent55

|dw:1441580817818:dw|

- mathstudent55

Correct. Your Part B is good.
4x^3 - 10x^2 - 7 is correct.

- MeowLover17

yes now how do i do part C?

- MeowLover17

please help

- mathstudent55

For Part C, you need to understand what this sentence means:
"polynomials are closed under addition and subtraction"

- MeowLover17

i don't understand what it means :/

- mathstudent55

Here is an example.
The set of integers is closed under addition, subtraction and multiplication.
That means that when you add two integers, or when you subtract integers, or when you multiply integers, the answer is an integer.
Integers are not closed under division because when you divide integers, you may get a non-integer answer. For example, 3/4 is not an integer.

- MeowLover17

oh i see

- mathstudent55

Now think of your problem and the set of all polynomials.
If you add two polynomials, is the sum always a polynomial?

- MeowLover17

So yes part A and B are closed under subtraction and addition since when i receive the sum of one problem it is still an integer.

- MeowLover17

Is that answer correct for part c?

- mathstudent55

Above, for Part A, we did add two polynomials. The sum was a polynomial.
This leads you to think that adding any polynomials together will result is a polynomial.

- mathstudent55

In Part B, we subtracted polynomials and the difference was a polynomial.
That makes us think that polynomials are closed under subtraction.

- MeowLover17

yes the sum is always a polynomial isnt it?

- mathstudent55

Your statement shows you have the right idea, but we are dealing with polynomials, not integers, so I'd modify it this way:
"Parts A and B show that polynomials are closed under addition and subtraction since when I added or subtracted polynomials, the result is still a polynomial."

- MeowLover17

Thanks you :)

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