PLEASE HELP!! The lengths of two sides of a triangle are shown.

Side 1: 8x2 − 5x − 2

Side 2: 7x − x2 + 3

The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

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)

9514 1404 393

Step-by-step explanation:

Part A:

  Side 1 + Side 2 = (8x^2 -5x -2) +(7x -x^2 +3)

  = (8 -1)x^2 +(-5+7)x +(-2+3)

  = 7x^2 +2x +1 . . . total length of side 1 and side 2

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Part B:

The perimeter is the total of all three sides, so the third side is the difference between the perimeter and the sum of the first two sides.

  Side 3 = Perimeter -(Side 1 +Side 2)

  = (4x^3 -3x^2 +2x -6) -(7x^2 +2x +1)

  = 4x^3 +(-3-7)x^2 +(2 -2)x +(-6 -1)

  = 4x^3 -10x^2 -7 . . . length of 3rd side

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Part C:

No. To show closure for all polynomials would require a demonstration involving all polynomials. We have shown closure for these particular polynomials.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.