Question

Ou are given the lengths of two sides of a triangle:

Side 1: 3x - 4x - 1
Side 2: 4x - x+

The perimeter of the triangle is described by the expression: 5x^2 - 2x + 3x - 8.

Part A: What is the total length of the two sides, Side 1 and Side 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.

Answer 1

The total length of the two sides of the triangle is 2x - 1. The length of the third side of the triangle is 5x^2 - 5x - 7. This confirms that polynomials are closed under addition and subtraction.

Step-by-step explanation:

To solve Part A, we need to find the expression for the total length of Side 1 and Side 2 in the triangle. We simplify the given expressions for Side 1, 3x - 4x - 1, which simplifies to -x - 1, and for Side 2, 4x - x+, simplifying this, we assume there is a typo and it should be 4x - x, which simplifies to 3x. Adding these together gives us a total length of 2x - 1 for the two sides combined.

For Part B, we'll use the expression for the perimeter of the triangle, 5x^2 - 2x + 3x - 8, and subtract the combined length of Side 1 and Side 2 from it. This simplification results in the length of the third side: 5x^2 - 5x - 7. Part C confirms that polynomials are indeed closed under addition and subtraction because the operations performed in Parts A and B have resulted in polynomials.