Brainliest ! the lengths of two sides of a triangle are shown below: side 1: 3x^2 − 4x − 1 side 2: 4x − x^2 + 5 the perimeter of the triangle is 5x^3 − 2x^2 + 3x − 8. 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)

1. For the total length of the two sides, you have to add the two polynomials together:


We can just combine like terms and we have our


2. We can set it up as:


All we need to do is subtract the polynomials to solve for y:


Simplify (subtract like terms):


That's the length of the 3rd side!

3. Yes, you can say that polynomials are closed under addition and subtraction based on Part A and Part B because whenever you add/subtract polynomials, you get an element from the same set. Indeed, they are 'closed'. 

Hope my answer helped! :)

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