Question

what is the additive inverse of the polynomial $-9xy^{2}+6x^{2}y - 5x^{3}$?\
\bigcirc $-9xy^{2}-6x^{2}y + 5x^{3}$\
\bigcirc $-9xy^{2}-6x^{2}y - 5x^{3}$\
\bigcirc $9xy^{2}+6x^{2}y + 5x^{3}$\
\bigcirc $9xy^{2}-6x^{2}y + 5x^{3}$

Explanation:

Step1: Recall additive inverse definition

The additive inverse of a polynomial \( P(x,y) \) is \( -P(x,y) \), which means we change the sign of each term.
Given polynomial: \( -9xy^2 + 6x^2y - 5x^3 \)

Step2: Find additive inverse

Change sign of each term:

• Sign of \( -9xy^2 \) becomes \( 9xy^2 \)
• Sign of \( +6x^2y \) becomes \( -6x^2y \)
• Sign of \( -5x^3 \) becomes \( +5x^3 \)

So the additive inverse is \( 9xy^2 - 6x^2y + 5x^3 \)

Answer:

D. \( 9xy^2 - 6x^2y + 5x^3 \) (assuming the options are labeled A to D as per standard, with the last option being D)