Question

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

Answer 1

option (b) is correct.

we get a polynomial
`3x^2-11x+8`

Explanation:

Given : Polynomial 5x -6 and
`3x^2-6x+2`.

We have to choose out of given options which shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from
`3x^2-6x+2`.

We first subtract the polynomial

`\Rightarrow 3x^2-6x+2-(5x-6))`

`\Rightarrow 3x^2-6x+2-5x+6`

similar terms are terms having same variables with same degree.

Here, -6x and -5x are similar

and 2 and 6 are similar.

Adding similar terms, we get,

`\Rightarrow 3x^2-11x+8`

Polynomial is an algebraic expression that can involves variables with non negative integer terms and constants.

Thus, we get a polynomial
`3x^2-11x+8`

Hence, option (b) is correct.

Answer 2

The correct answer is that 3x²-11x+8 will be a polynomial.

Explanation:
When we subtract polynomials, we combine like terms:
3x² is the only x² 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 3x²-11x+8. This is a polynomial, since it is made of monomials (none of the terms have a negative exponent or a radical sign).