Question

match each polynomial expression to its additive inverse.
$-6x^2 - x - 2$
$-6x^2 + x - 2$
$6x^2 - x + 2$
$6x^2 + x - 2$
$6x^2 + x + 2$
$-6x^2 - x + 2$
$6x^2 - x + 2$
$-6x^2 + x - 2$

Explanation:

Step1: Define additive inverse

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

Step2: Find inverse of $-6x^2 -x -2$

Multiply each term by $-1$:
$ -(-6x^2 -x -2) = 6x^2 + x + 2 $

Step3: Find inverse of $-6x^2 +x -2$

Multiply each term by $-1$:
$ -(-6x^2 +x -2) = 6x^2 -x + 2 $

Step4: Find inverse of $6x^2 -x +2$

Multiply each term by $-1$:
$ -(6x^2 -x +2) = -6x^2 +x -2 $

Step5: Find inverse of $6x^2 +x -2$

Multiply each term by $-1$:
$ -(6x^2 +x -2) = -6x^2 -x + 2 $

Answer:

1. $-6x^2 - x - 2 \longleftrightarrow 6x^2 + x + 2$
2. $-6x^2 + x - 2 \longleftrightarrow 6x^2 - x + 2$
3. $6x^2 - x + 2 \longleftrightarrow -6x^2 + x - 2$
4. $6x^2 + x - 2 \longleftrightarrow -6x^2 - x + 2$