To identify the additive inverse of each given polynomial, we need to change the sign of each term in the polynomial. The additive inverse of a polynomial [tex]\( P(x) \)[/tex] is another polynomial [tex]\( Q(x) \)[/tex] such that [tex]\( P(x) + Q(x) = 0 \)[/tex].
Let's go through each polynomial and find its additive inverse step-by-step:
1. Polynomial: [tex]\( -6x^2 - x - 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( 6x^2 + x + 2 \)[/tex]
2. Polynomial: [tex]\( 6x^2 - x + 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( -6x^2 + x - 2 \)[/tex]
3. Polynomial: [tex]\( 6x^2 + x - 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( -6x^2 - x + 2 \)[/tex]
4. Polynomial: [tex]\( -6x^2 - x + 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( 6x^2 + x - 2 \)[/tex]
5. Polynomial: [tex]\( -6x^2 + x - 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( 6x^2 - x + 2 \)[/tex]
6. Polynomial: [tex]\( -6x^2 + x - 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( 6x^2 - x + 2 \)[/tex]
7. Polynomial: [tex]\( 6x^2 + x + 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( -6x^2 - x - 2 \)[/tex]
8. Polynomial: [tex]\( 6x^2 - x + 2 \)[/tex]
- Additive inverse: Change the sign of each term.
- Inverse: [tex]\( -6x^2 + x - 2 \)[/tex]
Now, let's summarize the results in a list for clarity:
1. [tex]\( -6x^2 - x - 2 \)[/tex] → [tex]\( 6x^2 + x + 2 \)[/tex]
2. [tex]\( 6x^2 - x + 2 \)[/tex] → [tex]\( -6x^2 + x - 2 \)[/tex]
3. [tex]\( 6x^2 + x - 2 \)[/tex] → [tex]\( -6x^2 - x + 2 \)[/tex]
4. [tex]\( -6x^2 - x + 2 \)[/tex] → [tex]\( 6x^2 + x - 2 \)[/tex]
5. [tex]\( -6x^2 + x - 2 \)[/tex] → [tex]\( 6x^2 - x + 2 \)[/tex]
6. [tex]\( -6x^2 + x - 2 \)[/tex] → [tex]\( 6x^2 - x + 2 \)[/tex]
7. [tex]\( 6x^2 + x + 2 \)[/tex] → [tex]\( -6x^2 - x - 2 \)[/tex]
8. [tex]\( 6x^2 - x + 2 \)[/tex] → [tex]\( -6x^2 + x - 2 \)[/tex]
Thus, we have correctly matched each polynomial with its additive inverse.
