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

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

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

Answer

Explanation:

Step1: Recall the definition of additive inverse

The additive inverse of a polynomial (P(x)) is a polynomial (Q(x)) such that (P(x)+Q(x) = 0). If (P(x)=a_nx^n+\cdots+a_1x + a_0), then (Q(x)=-a_nx^n-\cdots - a_1x - a_0). For the polynomial (P(x)=-9xy^{2}+6x^{2}y - 5x^{3}), we change the sign of each term.

Step2: Find the additive inverse

The additive inverse (Q(x)) of (P(x)=-9xy^{2}+6x^{2}y - 5x^{3}) is obtained by multiplying each term by (- 1). [ \begin{align*} -(-9xy^{2}+6x^{2}y - 5x^{3})&=(-1)\times(-9xy^{2})+(-1)\times(6x^{2}y)+(-1)\times(-5x^{3})\ &=9xy^{2}-6x^{2}y + 5x^{3} \end{align*} ]

Answer:

(9xy^{2}-6x^{2}y + 5x^{3}) (the fourth option)