The lengths of two sides of a triangle are shown below:

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?

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

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

Part A:

Part B :

Step-by-step explanation:

Given: Two sides of a triangle  and perimeter

Side 1:

Side 2: or

Perimeter :

Part A :

Total length of side 1 and side 2 = Length of side 1+ Length of side 2

Therefore the sum of side 1 and side 2 is  

Part B :

Perimeter of triangle is = a+b+c where a,b,c are the sides of a triangle

Perimeter =Side 1+ Side 2 + Side 3  

So we have

Part C:

Now As we can see In part A and Part B

Addition of two polynomial is also a polynomial

Subtraction of two polynomial is also a polynomial

Therefore

Both Part A and Part B are closed under addition and subtraction

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

hope this !