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] ☐

Question

30-07-2024
Mathematics

Answered

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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 :

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GinnyAnsweridn GinnyAnsweridn · Answer 1 · 2024-07-30T10:10:21-04:00

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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