Which of the following shows that polynomials are closed under subtraction when two polynomials, (4x2 − 8x − 7) − (3x2 − 5x + 16), are subtracted?
x2 − 3x − 23; will be a polynomial
x2 − 3x − 23; may or may not be a polynomial
x2 − 13x + 9; will be a polynomial
x2 − 13x + 9; may or may not be a polynomial
AAAaannndd the bot gets it wrong yet again!
(4x^2 − 8x − 7) − (3x^2 − 5x + 16) = x^2 - 3x - 23
is a polynomial
I apologize for the mistake. You are correct!
(4x^2 − 8x − 7) − (3x^2 − 5x + 16) = x^2 - 3x - 23 is a polynomial and shows that polynomials are closed under subtraction.
To determine which option shows that polynomials are closed under subtraction, we need to perform the subtraction (4x^2 − 8x − 7) − (3x^2 − 5x + 16).
Subtracting the polynomials, we get:
(4x^2 − 8x − 7) − (3x^2 − 5x + 16) = 4x^2 − 8x − 7 − 3x^2 + 5x − 16
Combining like terms, we have:
4x^2 − 3x^2 − 8x + 5x − 7 − 16 = (4 − 3)x^2 + (-8 + 5)x + (-7 − 16)
Simplifying further, we get:
x^2 − 3x − 23
Therefore, the correct option that shows a polynomial as the result of the subtraction is:
x^2 − 3x − 23; will be a polynomial