Answer :
We start with the original polynomial:
[tex]$$
3x^3 - 2x^2 - x + 7.
$$[/tex]
To find its opposite, we multiply the whole polynomial by [tex]$-1$[/tex]:
[tex]$$
-(3x^3 - 2x^2 - x + 7).
$$[/tex]
Distributing the negative sign gives:
[tex]$$
-3x^3 + 2x^2 + x - 7.
$$[/tex]
Thus, two equivalent expressions for the opposite polynomial are:
[tex]$$
-\left(3x^3 - 2x^2 - x + 7\right) \quad \text{and} \quad -3x^3 + 2x^2 + x - 7.
$$[/tex]
This corresponds to option A.
[tex]$$
3x^3 - 2x^2 - x + 7.
$$[/tex]
To find its opposite, we multiply the whole polynomial by [tex]$-1$[/tex]:
[tex]$$
-(3x^3 - 2x^2 - x + 7).
$$[/tex]
Distributing the negative sign gives:
[tex]$$
-3x^3 + 2x^2 + x - 7.
$$[/tex]
Thus, two equivalent expressions for the opposite polynomial are:
[tex]$$
-\left(3x^3 - 2x^2 - x + 7\right) \quad \text{and} \quad -3x^3 + 2x^2 + x - 7.
$$[/tex]
This corresponds to option A.
