Which operation shows that polynomials are a closed system under subtraction?
(2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8
(2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
(2x^2+6x+1)−(3x^2+3x+9=(2x^2+6x−4)−(3x^2+3x+4)
The correct operation that shows that polynomials are closed under subtraction is:
(2x^2+6x+1)−(3x^2+3x+9)=(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
Which operation shows that polynomials are a closed system under addition?
(5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
(5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
(5x^2+2x+1)+(−2x^2+6x+4)=(−2x^2+2x+4)+(5x^2+6x+1)
(5x^2+2x+1)+(−2x^2+6x+4)=3x^2+8x+5
The correct operation that shows that polynomials are closed under addition is:
(5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
Which operation shows that polynomials are a closed system under addition?
(5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
(5x^2+2x+1)+(−2x^2+6x+4)=−3x^2+8x−3
(5x^2+2x+1)+(−2x^2+6x+4)=(−2x^2+2x+4)+(5x^2+6x+1)
(5x^2+2x+1)+(−2x^2+6x+4)=3x^2+8x+5
The correct operation that shows that polynomials are closed under addition is:
(5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
The operation that shows that polynomials are a closed system under subtraction is:
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
The correct operation that shows polynomials are a closed system under subtraction is:
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
To determine whether this operation demonstrates closure under subtraction for polynomials, we need to verify if the result of the subtraction is also a polynomial.
In this case, by subtracting the two polynomials, we obtain the polynomial -x^2+3x-8. This is indeed a polynomial because it is an algebraic expression with variables raised to non-negative powers and contains only addition, subtraction, and multiplication operations.
Therefore, the correct answer is:
(2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8