Question

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

$\circ$ $-9xy^2 - 6x^2y + 5x^3$
$\circ$ $-9xy^2 - 6x^2y - 5x^3$
$\circ$ $9xy^2 + 6x^2y + 5x^3$
$\circ$ $9xy^2 - 6x^2y + 5x^3$

Explanation:

Step1: Define additive inverse

The additive inverse of a polynomial $P$ is $-P$, which means multiplying each term by $-1$.

Step2: Apply to each term

Multiply each term of $-9xy^2 + 6x^2y - 5x^3$ by $-1$:
$(-1)(-9xy^2) + (-1)(6x^2y) + (-1)(-5x^3)$

Step3: Simplify each term

Calculate the product for each term:
$9xy^2 - 6x^2y + 5x^3$

Answer:

9xy² - 6x²y + 5x³ (the last option)