Answer:
Step-by-step explanation:
The length of one side of the triangle is 3x² - 2x - 1
The length of the other side of the triangle is 9x + 2x² - 3
Part A) The total length of the two sides, 1 and 2, of the triangle is
3x² - 2x - 1 + 9x + 2x² - 3
Collecting like terms, it becomes
3x² + 2x² + 9x - 2x - 1 - 3
5x² + 7x - 4
Part B
The perimeter of the triangle is
5x³ + 4x² - x - 3
The length of the third side is
5x³ + 4x² - x - 3 - (5x² + 7x - 4)
Expanding the brackets, it becomes
5x³ + 4x² - x - 3 - 5x² - 7x + 4
Collecting like terms, it becomes
5x³ - 5x² + 4x² - 7x - x - 3 + 4
5x³ - x² - 8x + 1
Part C
Yes, the polynomials are closed under addition and subtraction because these operations produced another polynomial.