Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x2 − 8x − 4 are added?
2x2 − 4x + 2; will be a polynomial
2x2 − 4x + 2; may or may not be a polynomial
2x2 − 12x − 10; will be a polynomial
2x2 − 12x − 10; may or may not be a polynomial
1 year ago
1 year ago
AAAaannndd the bot gets it wrong yet again!
4x + 6 + 2x^2 − 8x − 4 = 2x^2 - 4x + 2
is a polynomial
1 year ago
I apologize for the mistake in my previous response. You are correct that the sum of the two polynomials 4x + 6 and 2x^2 − 8x − 4 is 2x^2 - 4x + 2, which is a polynomial and shows that polynomials are closed under addition.
1 year ago
To determine if polynomials are closed under addition, we need to add the two given polynomials and check if the result is also a polynomial.
Adding the polynomials 4x + 6 and 2x^2 − 8x − 4:
(4x + 6) + (2x^2 − 8x − 4)
Combining like terms:
2x^2 - 4x - 4
The result 2x^2 - 4x - 4 is a polynomial.
Therefore, the correct answer is: 2x^2 − 4x + 2; will be a polynomial.
11 months ago
To determine whether polynomials are closed under addition, we need to check if the result of adding two polynomials remains a polynomial.
Let's add the two given polynomials, 4x + 6 and 2x^2 - 8x - 4.
To add polynomials, we combine like terms.
(4x + 6) + (2x^2 - 8x - 4)
Combine the x terms:
4x - 8x = -4x
Combine the constant terms:
6 - 4 = 2
The resulting polynomial is 2x^2 - 4x + 2.
Looking at the answer choices, we see that the polynomial 2x^2 - 4x + 2 is listed as "2x^2 − 4x + 2; will be a polynomial."
Therefore, the correct answer is "2x^2 − 4x + 2; will be a polynomial."