The lengths of two sides of a triangle are shown below:
Side 1: 3x2 - 2x - 1
Side 2: 9x + 2x2 - 3

The perimeter of the triangle is 5x3 + 4x2 - x - 3.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (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.

Question

The lengths of two sides of a triangle are shown below:
Side 1: 3x2 - 2x - 1
Side 2: 9x + 2x2 - 3

The perimeter of the triangle is 5x3 + 4x2 - x - 3.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (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.

anonymous · Answer

@campbell_st

anonymous · Answer

they really stretch to make these word problems don't they?
first step is to add $$3x^2-2x-1+9x+2x^2-3$$ aka combine like terms

anonymous · Answer

second step is to subtract that result from $$5x^3+4x^2-x-3$$

anonymous · Answer

third step is to say "yes" they are closed under addition and subtraction since you get a polynomial for an answer