Question

WILL AWARD MEDAL
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

Answer 1

@undeadknight26

Answer 2

@jim_thompson5910

Answer 3

@kirbykirby

Answer 4

(11x-2)(5x+3)?

Answer 5

im guessing i have no idea how to solve this -.-.....

Answer 6

Part A: just add the 2 sides together
(Side 1) + (side 2) = ?

Answer 7

how exactly? i need a walkthrough...because the answers are probably going to be wrong.

Answer 8

*the answers im getting are probably

Answer 9

\( (8x^2 - 5x - 2)+
(7x - x^2 + 3)
\)
Now just add up like-terms (add up the \(x^2\)-terms together, and add the \(x\)-terms together

Answer 10

7x^2+2x+1

Answer 11

yes :)

Answer 12

Now for part b), realize that the perimeter is the sum of all 3 sides of the triangle..
so (side 1) + (side 2) + (side 3) = \(\large 4x^3 - 3x^2 + 2x - 6\)
\((7x^2 + 2x + 1)+(\text {side 3})=4x^3-3x^2+2x-6\)

Answer 13

Isolate for (side 3)... so you subtract the perimeter from the sum of the 2 other sides

Answer 14

so its 4x^3-10x^2-7.THANKS!