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MeowLover17
 one year ago
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
 one year ago
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.

This Question is Closed

Hero
 one year ago
Best ResponseYou've already chosen the best response.0@MeowLover17, What is (8x^2  5x  2) + (7x  x^2 + 3) ?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Rearrange your terms to combine like terms with eachother. It makes it easier to evaluate.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1I got +6x^2+2x+1 @Hero

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Sorry my computer died

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Hello hero i got what i wrote above

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1So would that be the total length of the two sides??

Hero
 one year ago
Best ResponseYou've already chosen the best response.0You should have gotten 7x^2 + 2x + 1

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Oh sorry yes i see

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1So hero 7x^2 + 2x + 1 < This is my answer for part A correct?

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1how would i find the length of the third side?

Hero
 one year ago
Best ResponseYou've already chosen the best response.0To find the length of the third side subtract the result you got for part A from the perimeter.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1That's what i was thinking let me do that

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1so i would receive 4x^3+10^2+7?

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1for the length of the third side

Hero
 one year ago
Best ResponseYou've already chosen the best response.0Subtract this way: dw:1441579511663:dw

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1and if thats correct please help me with part C because i dont understand what its asking.

Hero
 one year ago
Best ResponseYou've already chosen the best response.0Yes. When you're subtracting one expression from the other, you have to flip the signs.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Oh i understand i forgot to change the signs

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1so i get 4x^32x^25x9

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1For the third side

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441580340586:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441580483756:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1To find the third side, subtract the sum of the lengths of the first two sides (Part A) from the perimeter.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Okay so i would recieve 4x^310x^27

Hero
 one year ago
Best ResponseYou've already chosen the best response.0Somehow I wrote the second term incorrectly.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1I just noticed that lol

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1But hero now that i have done gotten part B how do i do part 3?

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1Part B is 4x^310x^27 correct?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441580817818:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Correct. Your Part B is good. 4x^3  10x^2  7 is correct.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1yes now how do i do part C?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For Part C, you need to understand what this sentence means: "polynomials are closed under addition and subtraction"

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1i don't understand what it means :/

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here 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 noninteger answer. For example, 3/4 is not an integer.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now think of your problem and the set of all polynomials. If you add two polynomials, is the sum always a polynomial?

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1So 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
 one year ago
Best ResponseYou've already chosen the best response.1Is that answer correct for part c?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Above, 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
 one year ago
Best ResponseYou've already chosen the best response.1In Part B, we subtracted polynomials and the difference was a polynomial. That makes us think that polynomials are closed under subtraction.

MeowLover17
 one year ago
Best ResponseYou've already chosen the best response.1yes the sum is always a polynomial isnt it?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Your 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."
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