Question

The lengths of two sides of a triangle are shown below:

Side 1: 3x2 - 4x - 1
Side 2: 4x - x2 + 5

The perimeter of the triangle is 5x3 - 2x2 + 3x - 8.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer 1

@Hero can you help?

Answer 2

@sleepyjess
@sammixboo

Answer 3

@ganeshie8

Answer 4

which part are you stuck at ?

Answer 5

I think i have a and b but i want to make sure im right

Answer 6

good, what do you have for a and b ?

Answer 7

for a i have 2x^2+4 and part b i have 5x^3-4x^2+3x-4

Answer 8

part a is right
part b is wrong, but you're very close !

Answer 9

ok that's what I thought but what did I do wrong? can you explain

Answer 10

we're given two sides:
Side 1: \(3x^2 - 4x - 1\)
Side 2: \(4x - x^2 + 5\)

For part \(a\) :
Sum of the two sides can be obtained by adding both the sides :
Side1 + Side2 = \(3x^2 - 4x - 1\) + \(4x - x^2 + 5\) = \(\color{blue}{2x^2 + 4}\)

Answer 11

For part \(b\) :
Since the perimeter is given as \( 5x^3 - 2x^2 + 3x - 8.\), subtracting the sum of two sides from part \(a\) gives the third side : \[ 5x^3 - 2x^2 + 3x - 8- (\color{blue}{2x^2+4}) = 5x^3-4x^2+3x-12\]

Answer 12

oh ok I see where I got it wrong

Answer 13

So are we convinced adding/subtracting two polynomials gives another polynomial ?

Answer 14

no

Answer 15

wait yes sorry. I switched the question around

Answer 16

why not ?
In part \(a\), we have added two polynomials (\(3x^2 - 4x - 1,~~4x - x^2 + 5\)) and got another polynomial : \(\color{blue}{2x^2 + 4}\). This kinda shows that adding two polynomials gives another polynomial, yes ?

Answer 17

Ohk :)

Answer 18

so is that what i put that for part c? or is it something different?

Answer 19

Yes and add something like this :

Similarly part \(b\) convinces us that "subtracting" two polynomials gives us another polynomial. So can we say part \(a\) and part \(b\) show us that the polynomials are closed under addition and subtraction.

Answer 20

ok thanks soooooooo much!!!!!!!!!! and do you think you can help me with one more? its my last question @ganeshie8

Answer 21

Okay please ask in a separate thread :)