Certainly! To determine the additive inverses of the given polynomial expressions, we need to find the polynomial that, when added to the given polynomial, will result in zero.
Here are step-by-step matches of each polynomial expression to its additive inverse:
1. For the polynomial [tex]\( -6 x^2 + x - 2 \)[/tex]:
- The additive inverse is [tex]\( 6 x^2 - x + 2 \)[/tex].
- Therefore, [tex]\( -6 x^2 + x - 2 \)[/tex] matches with [tex]\( 6 x^2 - x + 2 \)[/tex].
2. For the polynomial [tex]\( 6 x^2 - x + 2 \)[/tex]:
- The additive inverse is [tex]\( -6 x^2 + x - 2 \)[/tex].
- Therefore, [tex]\( 6 x^2 - x + 2 \)[/tex] matches with [tex]\( -6 x^2 + x - 2 \)[/tex].
3. For the polynomial [tex]\( 6 x^2 + x + 2 \)[/tex]:
- The additive inverse is [tex]\( -6 x^2 - x - 2 \)[/tex].
- Therefore, [tex]\( 6 x^2 + x + 2 \)[/tex] matches with [tex]\( -6 x^2 - x - 2 \)[/tex].
4. For the polynomial [tex]\( 6 x^2 + x - 2 \)[/tex]:
- The additive inverse is [tex]\( -6 x^2 - x + 2 \)[/tex].
- Therefore, [tex]\( 6 x^2 + x - 2 \)[/tex] matches with [tex]\( -6 x^2 - x + 2 \)[/tex].
5. For the polynomial [tex]\( 6 x^2 - x + 2 \)[/tex]:
- The additive inverse is [tex]\( -6 x^2 + x - 2 \)[/tex] (note this polynomial appeared twice).
- Therefore, [tex]\( 6 x^2 - x + 2 \)[/tex] again matches with [tex]\( -6 x^2 + x - 2 \)[/tex].
6. For the polynomial [tex]\( -6 x^2 - x - 2 \)[/tex]:
- The additive inverse is [tex]\( 6 x^2 + x + 2 \)[/tex].
- Therefore, [tex]\( -6 x^2 - x - 2 \)[/tex] matches with [tex]\( 6 x^2 + x + 2 \)[/tex].
7. For the polynomial [tex]\( -6 x^2 - x + 2 \)[/tex]:
- The additive inverse is [tex]\( 6 x^2 + x - 2 \)[/tex].
- Therefore, [tex]\( -6 x^2 - x + 2 \)[/tex] matches with [tex]\( 6 x^2 + x - 2 \)[/tex].
Summarizing the matches:
[tex]\[
\begin{aligned}
&(-6 x^2 + x - 2, & 6 x^2 - x + 2) \\
&(6 x^2 - x + 2, & -6 x^2 + x - 2) \\
&(6 x^2 + x + 2, & -6 x^2 - x - 2) \\
&(6 x^2 + x - 2, & -6 x^2 - x + 2) \\
&(6 x^2 - x + 2, & -6 x^2 + x - 2) \\
&(-6 x^2 - x - 2, & 6 x^2 + x + 2) \\
&(-6 x^2 - x + 2, & 6 x^2 + x - 2) \\
\end{aligned}
\][/tex]
