To find the additive inverse of a polynomial expression, you simply change the sign of each term in the polynomial. Let's go through each polynomial expression step by step and find its additive inverse.
1. Polynomial: [tex]\(-6x^2 + x - 2\)[/tex]
- Terms: [tex]\(-6x^2\)[/tex], [tex]\(+x\)[/tex], [tex]\(-2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ 6x^2 - x + 2 \][/tex]
2. Polynomial: [tex]\(6x^2 - x + 2\)[/tex]
- Terms: [tex]\(6x^2\)[/tex], [tex]\(-x\)[/tex], [tex]\(+2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ -6x^2 + x - 2 \][/tex]
3. Polynomial: [tex]\(-6x^2 - x - 2\)[/tex]
- Terms: [tex]\(-6x^2\)[/tex], [tex]\(-x\)[/tex], [tex]\(-2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ 6x^2 + x + 2 \][/tex]
4. Polynomial: [tex]\(6x^2 + x - 2\)[/tex]
- Terms: [tex]\(6x^2\)[/tex], [tex]\(+x\)[/tex], [tex]\(-2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ -6x^2 - x + 2 \][/tex]
5. Polynomial: [tex]\(6x^2 + x + 2\)[/tex]
- Terms: [tex]\(6x^2\)[/tex], [tex]\(+x\)[/tex], [tex]\(+2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ -6x^2 - x - 2 \][/tex]
6. Polynomial: [tex]\(-6x^2 - x + 2\)[/tex]
- Terms: [tex]\(-6x^2\)[/tex], [tex]\(-x\)[/tex], [tex]\(+2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ 6x^2 + x - 2 \][/tex]
7. Polynomial: [tex]\(-6x^2 + x - 2\)[/tex]
- Terms: [tex]\(-6x^2\)[/tex], [tex]\(+x\)[/tex], [tex]\(-2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ 6x^2 - x + 2 \][/tex]
8. Polynomial: [tex]\(6x^2 - x + 2\)[/tex]
- Terms: [tex]\(6x^2\)[/tex], [tex]\(-x\)[/tex], [tex]\(+2\)[/tex]
- Additive inverse: Change the signs of each term
[tex]\[ -6x^2 + x - 2 \][/tex]
Now, let's match each polynomial to its additive inverse:
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]
