To find the additive inverse of the given polynomial [tex]\( -9xy^2 + 6x^2y - 5x^3 \)[/tex], we need to change the sign of each term in the polynomial.
1. The first term is [tex]\( -9xy^2 \)[/tex]. Changing the sign of [tex]\( -9xy^2 \)[/tex] gives [tex]\( 9xy^2 \)[/tex].
2. The second term is [tex]\( 6x^2y \)[/tex]. Changing the sign of [tex]\( 6x^2y \)[/tex] gives [tex]\( -6x^2y \)[/tex].
3. The third term is [tex]\( -5x^3 \)[/tex]. Changing the sign of [tex]\( -5x^3 \)[/tex] gives [tex]\( 5x^3 \)[/tex].
Therefore, the additive inverse of the polynomial [tex]\( -9xy^2 + 6x^2y - 5x^3 \)[/tex] is [tex]\( 9xy^2 - 6x^2y + 5x^3 \)[/tex].
So, the correct answer is:
[tex]\[9xy^2 - 6x^2y + 5x^3\][/tex]
The other options do not match the required additive inverse.
