The lengths of two sides of a triangle are shown.

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? 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)

(a)

(b)

(c)Yes

Step-by-step explanation:

Side 1:

Side 2:

Perimeter=

(a)Total length of the two sides, 1 and 2, of the triangle

(b)Length of the third side of the triangle

Since the perimeter is given, and we have the sum of the other two sides, we simply subtract it from the perimeter,

(c)When adding or subtracting polynomials, their variables and exponents do not change. Only the coefficients will change as in Part (a) and (b). Therefore, polynomials are closed under addition and subtraction.

the answer is b