Which polynomials are listed with their correct additive inverse? Check all that apply.

*x*2 + 3*x* – 2; –*x*2 – 3*x* + 2 

–*y*7 – 10; –*y*7 + 10 

6*z*5 + 6*z*5 – 6*z*4; (–6*z*5) + (–6*z*5) + 6*z*4

*x* – 1; 1 – *x*

(–5*x*2) + (–2*x*) + (–10); 5*x*2 – 2*x* + 10 

To determine if the listed polynomials are correctly paired with their additive inverses, we need to check if the sum of each pair results in zero.

### Checking Each Pair

1. \( x^2 + 3x - 2 \) and \( -x^2 - 3x + 2 \):
   \[ (x^2 + 3x - 2) + (-x^2 - 3x + 2) = 0 \]

2. \( -y^7 - 10 \) and \( -y^7 + 10 \):
   \[ (-y^7 - 10) + (-y^7 + 10) = -2y^7 \neq 0 \]

3. \( 6z^5 + 6z^5 - 6z^4 \) and \( (-6z^5) + (-6z^5) + 6z^4 \):
   \[ (6z^5 + 6z^5 - 6z^4) + (-6z^5 - 6z^5 + 6z^4) = 0 \]

4. \( x - 1 \) and \( 1 - x \):
   \[ (x - 1) + (1 - x) = 0 \]

5. \( (-5x^2) + (-2x) + (-10) \) and \( 5x^2 - 2x + 10 \):
   \[ (-5x^2 - 2x - 10) + (5x^2 - 2x + 10) = -4x \neq 0 \]

### Conclusion

The correctly paired additive inverses are:

1. \( x^2 + 3x - 2 \) and \( -x^2 - 3x + 2 \)
3. \( 6z^5 + 6z^5 - 6z^4 \) and \( (-6z^5) + (-6z^5) + 6z^4 \)
4. \( x - 1 \) and \( 1 - x \)

Would you like any more details or have any questions about this solution?

Here are 5 numbered questions you can ask:

1. How do you determine the additive inverse of a polynomial?
2. Can you show the step-by-step process of adding polynomials to check for additive inverses?
3. Why is it important to understand additive inverses in algebra?
4. What are common mistakes when finding the additive inverse of a polynomial?
5. How does the concept of additive inverses apply to solving equations?

**Tip:** Always verify the sum of a polynomial and its supposed additive inverse to ensure it equals zero. This confirms they are true additive inverses.

Explore the concept of additive inverses in polynomials with detailed examples. Check which polynomials are correctly paired with their additive inverses. Suitable for students in Grades 9-12.

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