Question

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

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.

Step2: Apply to given polynomial

Given polynomial: \( -9xy^2 + 6x^2y - 5x^3 \)
Multiply each term by \(-1\):
\(-1\times(-9xy^2) = 9xy^2\), \(-1\times(6x^2y) = -6x^2y\), \(-1\times(-5x^3) = 5x^3\)
So the additive inverse is \( 9xy^2 - 6x^2y + 5x^3 \).

Answer:

D. \( 9xy^2 - 6x^2y + 5x^3 \) (assuming the last option is D; if options are labeled differently, adjust the label but keep the expression)