Question

The lengths of two sides of a triangle are shown below:
Side 1: 3x^2 - 2x - 1
Side 2: 9x + 2x^2 - 3
The perimeter of the triangle is 5x^3 + 4x^2 - x - 3.

Part B: What is the length of the third side of the triangle?

Answer 1

Anyone? :/

Answer 2

Perimeter = length of side 1 + length of side 2 + length of side 3
length of side 3 = Perimeter - length of side 1 - length of side 2

Answer 3

Okay

Answer 4

length of side 3 = Perimeter - length of side 1 - length of side 2
= Perimeter - ( length of side 1 + length of side 2 )

Add the first two expressions given in the problem and then subtract it from the perimeter.

Answer 5

Okay

Answer 6

is it an equilateral ,isosceles, or scalene triangle

Answer 7

Perimeter = sum of all 3 sides
5x^3 + 4x^2 - x - 3 = 3x^2 - 2x - 1 + 9x + 2x^2 - 3 + y
solve for y the length of the 3rd side

Answer 8

equilateral = all 3 sides are equal
isosceles = 2 sides are equal
scalene = no sides are equal; all different lengths

Answer 9

They don't clarify what it is, it's just a triangle..

Answer 10

So, we have to subtract the perimeter by side 1 and side 2?

Answer 11

@triciaal ??

Answer 12

Someone?

Answer 13

you can tell from the lengths

subtract side 1 and side 2 from the perimeter to find the length of the 3rd side

Answer 14

Okay, can you take me through the subtraction?

Answer 15

5x^3 + 4x^2 - x - 3 = (3x^2 - 2x - 1 + 9x + 2x^2 - 3) + y

5x^3 + 4x^2 - x - 3 -(3x^2 - 2x - 1 + 9x + 2x^2 - 3) = y

Answer 16

5x^3 + 4 x^2 - x - 3 - 3 x^2 + 2 x + 1 - 9 x - 2 x^2 + 3 = y

Answer 17

now group like terms
5 x^3 + x^2 ( 4 -3 -2) +x(-1 + 2 -9) +(-3 + 1 + 3 ) = y
5 x^3 - x^2 -8 x + 1

Answer 18

Okay, then thats it?

Answer 19

yes

Answer 20

Oh! So the third side is 5 x^3 - x^2 -8 x + 1 ?

Answer 21

yes that's what I got

Answer 22

Okay thanks a ton!!!!!!!

Answer 23

if 2 + 3 + x = 7 how would you find x? same principle
x = 7 - (2 + 3)

Answer 24

@triciaal your great at this. I got the same thing

Answer 25

One last thing, does this show that polynomials are closed under addition and subtraction?

Answer 26

@lacrosseplayer22 thanks
@LearningIsAwesome you are welcome

Answer 27

yes

Answer 28

@triciaal thanks for being so smart and an expert
@LearningIsAwesome great jjob!

Answer 29

And thats because when a plynomial is added or subtracted it equals another polynomial right?

Answer 30

@triciaal

Answer 31

@triciaal is on a different problem

Answer 32

Well @lacrosseplayer22 do you know?

Answer 33

that depends

Answer 34

if its added or subtracting with an equal value on both sides yes

Answer 35

am I right @triciaal or not...or somewhat...

Answer 36

Okay! thanks SO much to both of you! Especially @triciaal :)

Answer 37

wait a sec. I mat not be right. im waiting for @triciaal 's response

Answer 38

I think it shows closure because when a polynomial is subtracted or added it equals another polynomial, right?

Answer 39

an equation is an equation. a + b = c c-b=a and c - a = b
I am looking for the textbook version

Answer 40

https://learnzillion.com/lessons/3138-determine-which-operations-are-closed-for-polynomials

Answer 41

Oh, so they are closed!