Question 2 (Essay Worth 10 points) (06.02 MC) The lengths of two sides of a triangle are shown. Side 1: 8x²-5x-2

Question

Question 2 (Essay Worth 10 points)
(06.02 MC)
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)

Gerda · Answer

Answer:   See below ~   Step-by-step explanation:   Part A :   ⇒ Total Length = Side 1 + Side 2  ⇒ Total Length = (8x² - 5x - 2) + (7x - x² + 3)  ⇒ Total Length = 7x² + 2x + 1     =============================================================    Part B :   ⇒ Length of 3rd side = Perimeter - Part A solution  ⇒ Length of 3rd side = 4x³ - 3x² + 2x - 6 - (7x² + 2x + 1)  ⇒ Length of 3rd side = 4x³ - 10x² - 7     ===========================================================    Part C :   ⇒  Yes   ⇒ It shows they are closed under  addition  and  subtraction  because no new values come into the equations

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