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Match each polynomial expression to its additive inverse.

1. [tex]\(-6x^2 + x - 2\)[/tex] ☐
2. [tex]\(6x^2 - x + 2\)[/tex] ☐
3. [tex]\(6x^2 + x + 2\)[/tex] ☐
4. [tex]\(6x^2 + x - 2\)[/tex] ☐
5. [tex]\(6x^2 - x + 2\)[/tex] ☐
6. [tex]\(-6x^2 - x - 2\)[/tex] ☐
7. [tex]\(-6x^2 - x + 2\)[/tex] ☐

Sagot :

GinnyAnsweridn
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]
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