Which operation shows that polynomials are a closed system under addition?(1 point)
Responses
(2x2+6x+1)+(3x2+3x+9)=(2x2+3x+1)+(3x2+6x+9)
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=(2x2+3x2)+(6x+3x)+(1+9)
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals negative x squared plus 3 x minus 8
(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10
Bot GPT 3.5 is correct
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The correct response is:
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x + 1) + (3x^2 + 6x + 9)
The correct response is:
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x + 1) + (3x^2 + 6x + 9)
Explanation:
To show that polynomials are a closed system under addition, we need to demonstrate that adding two polynomials will result in another polynomial. In this case, we have two polynomials: (2x^2 + 6x + 1) and (3x^2 + 3x + 9).
To perform the addition, we add the corresponding terms of the polynomials. This means adding the coefficients of like terms:
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x^2) + (6x + 3x) + (1 + 9)
This simplifies to:
5x^2 + 9x + 10
Therefore, by adding the two given polynomials, we obtain another polynomial (5x^2 + 9x + 10). This demonstrates that polynomials are closed under addition.