Question

3x2 − 4x − 1

Answer 1

i just need help figuring this out

Answer 2

factorization right?

Answer 3

i dont know, its part of the 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)
but i just need help with that part

Answer 4

can you help?

Answer 5

can you help

Answer 6

@phi

Answer 7

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

to do that , add the two sides

Answer 8

to add , write down the length of 1 side, put in a "+" sign, and the write the other side

Answer 9

side 1 is \( 3x^2 − 4x − 1 \)
side 2 is \( 4x − x^2 + 5 \)

Answer 10

2x^2+4

Answer 11

yes. notice the "add part" is simple. you write
\[ 3x^2 − 4x − 1 + 4x − x^2 + 5 \]
the harder part is combining "like terms" and making it look simple

Answer 12

Yea

Answer 13

next part. perimeter is the sum of all 3 sides
to find the 3rd side, it is what is left over after subtracting off the two other sides from the total length (i.e. from the perimeter)

Answer 14

wait so part a is just 2x^2+4 ?

Answer 15

in other words:
perimeter - (two sides)
5x3 − 2x2 + 3x − 8 - (2x^2+4)

Answer 16

2x^2 + 4 is the sum of the first 2 sides
when we add the 3rd side we get the perimeter

2x^2+4 + (3rd side) = perimeter
or "solving for (3rd side)
(3rd side) = perimeter - (2x^2+4)

Answer 17

5x3−4x2+3x−12

Answer 18

most excellent.
the tricky part with subtraction is to remember the minus applies to all of the terms in (2x^2+4)

Answer 19

So, is that part B?

Answer 20

the last part, just say if you start with polynomials and add or subtract them, the answer is a polynomial... so polynomials are closed under addition and subtraction

Answer 21

your answer for B is good

Answer 22

i dont understand part C

Answer 23

polynomials are closed under addition and subtraction

means: if you add two (or subtract) two polynomials, the answer will be a polynomial

sometimes operations are closed... sometimes not.
for example. integers are closed under add/subtract
integer + integer will always give an integer answer.
on the other hand, integers are not closed under division
example 4 / 2 is 2 so that is ok, but we could also do 2/4 = 1/2 and that is not an integer. so not closed.

Answer 24

so your saying it will have 2 or more terms?

Answer 25

@phi

Answer 26

when we talk about polynomials we have to allow for 0 ,1 or more terms
(which contradicts the "poly" (Greek for many) definition ), but people want polynomials closed under subtraction, and if we did not allow 0
then
x^2 + x - (x^2+x) =0
would have two polynomials giving a non-polynomial answer. Solution:
let 0 be part of the polynomials.

any way, the answer to part C is, both adding and subtracting polynomials gave a polynomial as an answer.

Answer 27

do x^2 + x - (x^2+x) =0 and that will be the answer?

Answer 28

for part c

Answer 29

no. (that was an extra example)

for part C, say that the answers to part A (adding) and part B (subtracting)
both started with polynomials, and had a polynomial as an answer.

Answer 30

yea

Answer 31

showing that polynomials are closed under subtraction/addition

Answer 32

okay