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)
(10 points)

Answer 1

Part A

`3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}`

Part B

`(5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}`

Part C

No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.