Question

The lengths of two sides of a triangle are shown below:
Side 1: 5x2 + 2x - 3
Side 2: 8x - 3x2 + 2

The perimeter of the triangle is 2x3 - 5x2 + 4x - 8.

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.

Answer 1

*** What is the total length of the two sides, 1 and 2 ?***
I would add the two sides. in other words, put a + sign in like this
\[ 5x^2 + 2x - 3 + 8x - 3x^2 + 2\]

of course, they want you to simplify it by combining "like terms"

Answer 2

cool! so after you put the plus sighn and combined what would you do as the next step?

Answer 3

first, what did you get after simplifying?

Answer 4

give me just a second to check

Answer 5

actually i don't think i simplified mine at all

Answer 6

in these i do something called foiling.

Answer 7

people start with the "highest order" which is the term with x to the biggest exponent
in your problem those are the terms with x^2

so circle the x^2 terms

Answer 8

be sure to include the minus sign

Answer 9

okay! (:

Answer 10

\[ 5x^2 - 3x^2 \]
that says you have 5 x^2 's , take away 3 of them. how many x^2 's do you have?

Answer 11

3? wouldn't that get me x? or -x^1 or something simulare?

Answer 12

2 x^2
it is the same kind of problem as 5 horses -3 horses is 2 horses

except we are counting x^2

Answer 13

\[ 5x^2 + 2x - 3 + 8x - 3x^2 + 2 \\
\text{ combine } 5x^2 -3x^2 \text{ to get}\\
2x^2 + 2x - 3 + 8x + 2\]

Answer 14

now combine the terms with just 1 x in them
can you do that ?

Answer 15

have you ever done a process called foiling?

Answer 16

that is what i do and in this equation can i do that?

Answer 17

FOIL is a way to remember how to multiply (a+b)(c+d) (or anything with that pattern)
we don't do that here.

we are adding (which is easier).
can you add the terms
2x+8x
?

Answer 18

2 x's plus 8 more x's is how many x's ?
and be sure to include the "x" in the answer.

Answer 19

2x^2 +10x-5 ?

Answer 20

yes 2x+8x is 10x

now do the numbers

Answer 21

notice it is -3 (don't forget the minus sign) and +2

Answer 22

\[ 5x^2 + 2x - 3 + 8x - 3x^2 + 2 = ?\]

Answer 23

oh wait it would be 1 because3 is negitive

Answer 24

i see
hang on

Answer 25

write down
-3+2
or 2+ -3
either way
what is the answer?

Answer 26

the answer is -1

Answer 27

yes. now you can write down the entire answer (simplified version) of
\[ 5x^2 + 2x - 3 + 8x - 3x^2 + 2 \]

Answer 28

cool!! 2x^2-1x+1?

Answer 29

i might have missed something

Answer 30

Do we have to go over the problem again?
first combine the x^2 terms
then the x terms
then the numbers

Answer 31

you don't have to cover the whole thing again. i had an issue with this problem in the past. the reason i am mostly confused is because of the signs they throw me off and end up giving me a wrong result! all i really need to know is when you combined like terms, what decides the sighns?

Answer 32

I change things like
4-2 into 4 + -2

or
3x - x into 3x + -1x
does that make sense?

Answer 33

yes i think so!!

Answer 34

the minus sign goes with the number (or letter)

Answer 35

okay! thanks!! i have to get going to the next class!! you gave me plenty of info and i should be able to wright this out!! Thanks!!!

Answer 36

ok

Answer 37

bye!