Question

Side1 : 3x^2 − 4x − 1 (^to the second power)

Side2: 4x − x^2 + 5 (^to the second power)
Perimeter of the triangle is: 5x^3 -2x^2+3x-8 (^to the second power)

Please Explain:
Part A: What is the total lenge of sides 1 and 2 of the triangle?
Part B: What is the length of the 3rd side of traingle?
Part C: Is Part A and Part B identify the polynomials are closed under addition and subtraction-please show math

Answer 1

9514 1404 393

Answer:

A. 2x^2 +4

B. 5x^3 -4x^2 +3x -12

C. addition and subtraction of polynomials result in polynomials (closed)

Explanation:

A. The total of the two side lengths is ...

(3x^2 -4x -1) +(-x^2 +4x +5) = (3 -1)x^2 +(-4+4)x +(-1+5) = 2x^2 +4

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B. The length of the third side is the difference between the total for all three sides and the total for the given two sides:

(5x^3 -2x^2 +3x -8) - (2x^2 +4) = 5x^3 +(-2-2)x^2 +3x +(-8-4)

= 5x^3 -4x^2 +3x -12

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C. Addition of the two polynomials results in a polynomial. Subtraction of the two polynomials results in a polynomial. There is nothing here to indicate the set of polynomials is not closed under addition and subtraction.