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The lengths of two sides of a triangle are shown below
Side 1: 3x^2-2x-1
Side 2: 9x + 2x^2-3
The perimeter of the triangle is 5x^3 4x^2 x3

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (4 points)

Part c: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justity your answer. (2 points)

Respuesta :

HomertheGenius
Part A:( 3 x² - 2 x - 1 ) + ( 9 x + 2 x² - 3 ) = = 3 x² + 2 x² - 2 x + 9 x - 1 - 3 = = 5 x² + 7 x - 4Part B :( 5 x³+ 4 x² + x + 3 ) - ( 5 x² + 7 x - 4 ) = = 5 x³ + 4 x² - 5 x² + x - 7 x + 3 + 4 = = 5 x³ - x² - 6 x + 7Part C:Answers in Part A and in Part B shows that the polynomials are closed under addition and subtraction.Closure under addition: while adding polynomials the variables and their exponents do not change. Only their coefficients will possibly change.Closure under subtraction: while subtracting polynomials the variables and their exponents do not change, only their coefficients will possibly change.

mkay140

Answer:

Part A:

( 3 x² - 2 x - 1 ) + ( 9 x + 2 x² - 3 ) =

= 3 x² + 2 x² - 2 x + 9 x - 1 - 3

= 5 x² + 7 x - 4

Part B :

( 5 x³+ 4 x² + x + 3 ) - ( 5 x² + 7 x - 4 ) =

= 5 x³ + 4 x² - 5 x² + x - 7 x + 3 + 4 =

= 5 x³ - x² - 6 x + 7

Part C: Polynomials are always closed if under addition or subtraction. Both parts A and B are polynomials.

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