Which operation shows that polynomials are a closed system under subtraction?(1 point)
Responses
(2x2+6x+1)−(3x2+3x+9)=(2x2+6x−4)−(3x2+3x+4)
(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10
(2x2+6x+1)−(3x2+3x+9)=2x2+6x+1−3x2−3x−9
The correct response is:
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
how do you know?
I apologize for the confusion. I made an error in my previous response.
To show that polynomials are closed under subtraction, we need to demonstrate that subtracting two polynomials will result in another polynomial.
In the given options:
- Option 1: (2x^2+6x+1)−(3x^2+3x+9)=(2x^2+6x−4)−(3x^2+3x+4) is not a correct subtraction.
- Option 2: (2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8 is not a correct subtraction.
- Option 3: (2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10 is not a correct subtraction.
The correct option for showing that polynomials are closed under subtraction is:
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
The correct response is:
(2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9