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.

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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.

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

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Rearrange your terms to combine like terms with eachother. It makes it easier to evaluate.
I got +6x^2+2x+1 @Hero
Sorry my computer died
Hello hero i got what i wrote above
So would that be the total length of the two sides??
You should have gotten 7x^2 + 2x + 1
Oh sorry yes i see
So hero 7x^2 + 2x + 1 <- This is my answer for part A correct?
how would i find the length of the third side?
To find the length of the third side subtract the result you got for part A from the perimeter.
That's what i was thinking let me do that
so i would receive -4x^3+10^2+7?
for the length of the third side
Subtract this way: |dw:1441579511663:dw|
ok
-4x^3 -4x^2-5x-3
Is what i got
and if thats correct please help me with part C because i dont understand what its asking.
What is 4x^3 minus zero?
|dw:1441579942249:dw|
+4x^3
4x^3 -4x^2-5x-3
What is -3x^2 -(-x^2) ?
-2x^2
Yes. When you're subtracting one expression from the other, you have to flip the signs.
Oh i understand i forgot to change the signs
Yes :/
so i get 4x^3-2x^2-5x-9
For the third side
|dw:1441580340586:dw|
|dw:1441580483756:dw|
To find the third side, subtract the sum of the lengths of the first two sides (Part A) from the perimeter.
Okay so i would recieve 4x^3-10x^2-7
Right?
Somehow I wrote the second term incorrectly.
I just noticed that lol
But hero now that i have done gotten part B how do i do part 3?
Part B is 4x^3-10x^2-7 correct?
|dw:1441580817818:dw|
Correct. Your Part B is good. 4x^3 - 10x^2 - 7 is correct.
yes now how do i do part C?
please help
For Part C, you need to understand what this sentence means: "polynomials are closed under addition and subtraction"
i don't understand what it means :/
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.
oh i see
Now think of your problem and the set of all polynomials. If you add two polynomials, is the sum always a polynomial?
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.
Is that answer correct for part c?
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.
In Part B, we subtracted polynomials and the difference was a polynomial. That makes us think that polynomials are closed under subtraction.
yes the sum is always a polynomial isnt it?
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."
Thanks you :)

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