Which of the following shows that polynomials are closed under subtraction when polynomial 5x - 6 is subtracted from 3x2 - 6x + 2?

answers:

3x2 - 11x + 8 may or may not be a polynomial

3x2 - 11x + 8 will be a polynomial

3x2 - x + 4 may or may not be a polynomial

3x2 - x + 4 will be a polynomial

The correct answer is that 3x ² - 11x+8 will be a polynomial.

Explanation:

When we subtract polynomials, we combine like terms:

3x ² is the only x ² term we have.

We have - 6x and subtract 5x from it; this gives us - 11x.

We have 2 and subtract - 6 from it; when we subtract a negative, we add the opposite, which means we have 2--6=2+6=8.

This gives us 3x ² - 11x+8. This is a polynomial, since it is made of monomials (none of the terms have a negative exponent or a radical sign).