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The lengths of two sides of a triangle are shown.

Side 1: 3x2 − 4x − 1

Side 2: 4x − x2 + 5

The perimeter of the triangle is 5x3 − 2x2 + 3x − 8.

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 :

semsee45

Answer:

A)  [tex]2x^2+4[/tex]

B) [tex]5x^3-4x^2+3x-12[/tex]

C) Yes

Step-by-step explanation:

Perimeter: the distance all the way around the outside of a 2D figure.

Therefore, to calculate the perimeter, add up the lengths of all the sides.

Given expressions:

  • Triangle side 1:  [tex]3x^2-4x-1[/tex]
  • Triangle side 2:   [tex]4x-x^2+5[/tex]
  • Perimeter:   [tex]5x^3-2x^2+3x-8[/tex]

Part A

[tex]\begin{aligned}\sf side\:1+side\:2 & =(3x^2-4x-1)+(4x-x^2+5)\\ & =3x^2-4x-1+4x-x^2+5\\ & =3x^2-x^2-4x+4x-1+5\\ & =2x^2+4\end{aligned}[/tex]

Part B

[tex]\begin{aligned}\sf side\:3 & =\sf perimeter-(side\:1+side\:2)\\ & =(5x^3-2x^2+3x-8)-(2x^2+4)\\& = 5x^3-2x^2+3x-8-2x^2-4\\& = 5x^3-2x^2-2x^2+3x-8-4\\ & = 5x^3-4x^2+3x-12\end{aligned}[/tex]

Part C

Polynomials and closure:  Polynomials will be closed under an operation if the operation produces another polynomial.

So as the addition and subtraction of the given polynomials has produced another polynomial, then the polynomials are closed under addition and subtraction.

allenweller167

Answer:

he or she is right above

Step-by-step explanation:

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