Question

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

Side 1: 3x2 − 2x − 1

Side 2: 9x + 2x2 − 3

The perimeter of the triangle is 5x3 + 4x2 − x − 3.

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)

(I ONLY NEED HELP WITH PART B AND C)

Answer 1

Part A ; Just add
3x2 − 2x − 1 + 9x + 2x2 − 3

yes you are correct

Answer 2

Part B ;- its perimeter - sum of other 2 sides
= 5x^3 + 4x^2 − x − 3 - (5x^2+7x−4)
= 5x^3 + 4x^2 - x - 3 - 5x^2 - 7x + 4
- note that you distribute the negative over the parentheses so some signs change

Answer 3

= 5x^3 - x^2 - 8x + 1

Answer 4

yes
- note when you subtract polynomials first put the second one in parentheses

Answer 5

Being closed under addition and subtraction means that the result os adding and subtracting polynomials results in another polynomial. And these 2 operations which we have done show that to be the case.

Answer 6

*of not os

Answer 7

Thank you so much for your help! I finally understand how to do it now :)))

Answer 8

yw