Question

The lengths of two sides of a triangle are shown. Side 1: 3x2 − 4x − 1 Side 2: 4x − x2 5 The perimeter of the triangle is 5x3 − 2x2 3x − 8. 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).

Answer 1

The following results are;

• The total length of the two sides is $\rm 2x^2 + 4$.
• The length of the third side is $\rm y = 5x^3 -4x^2 + 3x -12$.
• Yes, Part A and Part B show that the polynomials are closed under addition and subtraction.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In a triangle, the sides and perimeter are given.

$\rm Side\ 1: 3x^2 - 4x - 1 \\\\Side\ 2: - x^2 + 4x + 5\\\\Perimeter = 5x^3 - 2x^2 +3x - 8$

a.  The total length of the two sides will be

$\rm 3x^2 - 4x - 1 + (- x^2 + 4x + 5) \\\\\rm 3x^2 - 4x - 1 - x^2 + 4x + 5) \\\\2x^2 + 4$

The total length of the two sides is $\rm 2x^2 + 4$.

b.  Then a length of the third side (y) will be

$\rm 3x^2 - 4x - 1 + (- x^2 + 4x + 5) + y = 5x^3 - 2x^2 +3x - 8$

On solving for y, we have

$\rm y = 5x^3 - 2x^2 +3x - 8 -( 3x^2 - 4x - 1) - (- x^2 + 4x + 5)\\\\y = 5x^3 - 2x^2 +3x - 8 - 3x^2 +4x + 1 + x^2 - 4x - 5\\\\ y = 5x^3 -4x^2 + 3x -12$

The length of the third side is $\rm y = 5x^3 -4x^2 + 3x -12$.

c.  Yes, Part A and Part B show that the polynomials are closed under addition and subtraction.

More about the triangle link is given below.

brainly.com/question/25813512