College

What is the additive inverse of the polynomial [tex]$-9 x y^2 + 6 x^2 y - 5 x^3$[/tex]?

A. [tex]$-9 x y^2 - 6 x^2 y + 5 x^3$[/tex]
B. [tex]$-9 x y^2 - 6 x^2 y - 5 x^3$[/tex]
C. [tex]$9 x y^2 + 6 x^2 y + 5 x^3$[/tex]
D. [tex]$9 x y^2 - 6 x^2 y + 5 x^3$[/tex]

Answer :

To find the additive inverse of the polynomial [tex]\(-9xy^2 + 6x^2y - 5x^3\)[/tex], you need to change the sign of each term in the polynomial. Let's go through it step-by-step:

1. Original Polynomial: [tex]\(-9xy^2 + 6x^2y - 5x^3\)[/tex]

2. Change the Sign of Each Term:
- The first term [tex]\(-9xy^2\)[/tex] becomes [tex]\(9xy^2\)[/tex].
- The second term [tex]\(6x^2y\)[/tex] becomes [tex]\(-6x^2y\)[/tex].
- The third term [tex]\(-5x^3\)[/tex] becomes [tex]\(5x^3\)[/tex].

3. Resulting Polynomial: When you change the signs of all terms, the additive inverse of the polynomial becomes [tex]\(9xy^2 - 6x^2y + 5x^3\)[/tex].

Therefore, the additive inverse of the given polynomial is:
[tex]\[ 9xy^2 - 6x^2y + 5x^3 \][/tex]

From the choices provided, this corresponds to:
[tex]\[ 9xy^2 + 6x^2y + 5x^3 \][/tex]

Make sure to double-check the options to find the correct one based on the inverse you calculated.

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