The lengths of two sides of a triangle are shown below:
side 1: 3x^2 − 2x − 1
side 2: 9x + 2x^2 − 3
the perimeter of the triangle is 5x^3 + 4x^2 − 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)

Part A : add side 1 to side 2
8x^2 - 5x - 2 + 7x - x^2 + 3 combine like terms
7x^2 + 2x + 1 <=== total of side 1 + side 2

part B : since perimeter is the sum of all sides, we can find the third side by subtracting the sum of the 2 sides (from part A) from the perimeter.
4x^3 - 3x^2 + 2x - 6 - (7x^2 + 2x + 1)...distribute thru the parenthesis
4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1 =combine like terms
4x^3 - 11x^2 - 7 <===length of 3rd side

part C : Polynomials are closed under addition and subtraction because when adding/subtracting polynomials, the result is another polynomial.