Question

Can someone solve this for me???

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

Side 1: 3x^2 − 2x − 5

Side 2: 7x - 2x^2 − 3

The perimeter of the triangle is 5x^3 + 4x^2 − x − 3.

Part A: What is the total length of the two sides, 1 and 2, of the triangle?
Answer: x^2+5x-8

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

With this, I can't solve B..

Answer 1

Part A: x^2 + 5x - 8

Part B: 5x^3 + 3x^2 - 6x + 5

Explanation:

Part A:

To find the total of side 1 and 2, add the two expressions which represent each side. Combine like terms to simplify.

3x^2 − 2x − 5 + (7x - 2x^2 − 3)

3x^2 - 2x^2 -2x + 7x -5 + -3

x^2 + 5x - 8

Part B:

To solve for the third side of a triangle using its perimeter, subtract the lengths of two of its sides from its perimeter. The perimeter is 5x^3 + 4x^2 − x − 3. Subtract 3x^2 − 2x − 5 and 7x - 2x^2 − 3. The remaining expression is the third side. Combine like terms to simplify.

5x^3 + 4x^2 − x − 3 - (3x^2 − 2x − 5) - (7x - 2x^2 − 3)

5x^3 + 4x^2 - x - 3 - 3x^2 + 2x + 5 - 7x + 2x^2 + 3

5x^3 + (4x^2 -3x^2 + 2x^2) + (-x + 2x - 7x) + (-3 + 5 + 3)

5x^3 + 3x^2 - 6x + 5