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? (5 points)

Part B: What is the length of the third side of the triangle(Hint: Take the total perimeter and subtact off the total lenght of the other 2 sides found in Part A)?

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

Part A: 5x² + 7x - 4

Part B: 5x³ - x² - 8x + 1

Part C: Yes.

Step-by-step explanation:

Part A: The length of two sides of a triangle are given by

Side 1: 3x² - 2x - 1

Side 2: 9x + 2x² - 3

Now, the total length of the two sides, 1 and 2, of the triangle will be

= (3x² - 2x - 1) + (9x + 2x² - 3)

= 5x² + 7x - 4 (Answer)

Part B: If the length of the third side is y and the perimeter of the triangle is (5x³ + 4x² - x - 3), then

y = (5x³ + 4x² - x - 3) - (5x² + 7x - 4) = 5x³ - x² - 8x + 1 (Answer)

Part C: The answers in the part A and part B are closed under addition and subtraction. (Answer)

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step-by-step explanation: