Which operation shows that polynomials are a closed system under addition? (1 point)
(5x ^ 2 + 2x + 1) + (- 2x ^ 2 + 6x + 4) =(5x^ 2 -2x^ 2 )+(2x+6x)+(1\
(5x ^ 2 + 2x + 1) + (- 2x ^ 2 + 6x + 4) = (- 2x ^ 2 + 2x + 4) + (5x ^ 2 + 6x)
(5x ^ 2 + 2x + 1) + (- 2x ^ 2 + 6x + 4) = 3x ^ 2 + 8x + 5
(-2x²+6x+4)=-3x² + 8x - 3 (5x² + 2x + 1) + (-2x²+6x+4) -3x²+8x
The operation that shows that polynomials are a closed system under addition is:
(5x^2 + 2x + 1) + (-2x^2 + 6x + 4) = 3x^2 + 8x + 5
The operation that shows that polynomials are a closed system under addition is the addition itself. To perform the addition of two polynomials, you simply add their respective like terms together.
In this specific example, you have the expression (5x^2 + 2x + 1) + (-2x^2 + 6x + 4). To add these polynomials, you can rearrange the terms to group like terms together:
(5x^2 + 2x + 1) + (-2x^2 + 6x + 4) = (5x^2 - 2x^2) + (2x + 6x) + (1 + 4)
Now, you can simplify each group of like terms:
(5x^2 - 2x^2) = 3x^2
(2x + 6x) = 8x
(1 + 4) = 5
Putting it all together, the sum is:
(5x^2 + 2x + 1) + (-2x^2 + 6x + 4) = 3x^2 + 8x + 5
Therefore, the operation of addition shows that polynomials are a closed system under addition in this case.
The operation that shows that polynomials are a closed system under addition is:
(5x^2 + 2x + 1) + (-2x^2 + 6x + 4) = (-2x^2 + 2x + 4) + (5x^2 + 6x) = 3x^2 + 8x + 5