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The lengths of two sides of a triangle are shown.

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? Show your work.(4 points)

Part B: What is the length of the third side of the triangle? Show your work. (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)

Respuesta :

Answer:

See below ↓↓↓

Step-by-step explanation:

Part A

Total length = Side 1 + Side 2

  • 3x² - 2x - 1 + 9x + 2x² - 3
  • 3x² + 2x² + 9x - 2x - 1 - 3
  • 5x² + 7x - 4

Part B

Length of 3rd side = Perimeter - [Side 1 + Side 2]

  • L = 5x³ + 4x² - x - 3 - [5x² + 7x - 4]
  • L = 5x³ + 4x² - x - 3 - 5x² - 7x + 4
  • L = 5x³ - x² - 8x + 1

Part C

Yes, as the resulting polynomial has a finite value we can conclude that polynomials are closed under addition and subtraction.

Part A: The total length of the two sides of the triangle is [tex]5x^2+7x-4[/tex]. This is obtained by adding the given two sides.

Part B: The length of the third side is [tex]5x^3-x^2-8x+1[/tex]. This is obtained by subtracting the sum of two sides from the perimeter of the triangle.

Part C: Yes, the Part A and Part B answers show that the polynomials are closed under addition and subtraction. This is because the expressions have like terms.

Polynomials:

  • These are the expressions that are formed with constants, coefficients, and variables.
  • based on the highest degree of the variable in the expressions, the polynomials are classified into many types.

Calculation:

Given that, a triangle has two sides of length [tex]3x^2-2x-1[/tex] and [tex]9x+2x^2-3[/tex]

The perimeter of the triangle is [tex]5x^3+4x^2-x-3[/tex]

Part A:

To find the total length of two sides, adding the two side

⇒ [tex](3x^2-2x-1)+9x+2x^2-3\\[/tex]

⇒ [tex]5x^2+7x-4[/tex]

(adding the like terms w.r.t their sign)

Part B:

To find the length of the third side, subtract the sum of two sides from the perimeter.

⇒ [tex](5x^3+4x^2-x-3)-(5x^2+7x-4)[/tex]

⇒ [tex]5x^3-x^2-8x+1[/tex]

Part C:

From Part A and Part B, it is proved that the polynomials undergo addition and subtraction. Hence, it is justified.

Therefore, Part A, Part B, and Part C were obtained.

Learn more about polynomials here:

https://brainly.com/question/1315292

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