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

x^{2} + 3x – 2; –x^{2} – 3x + 2

–y^{7} – 10; –y^{7} + 10

6z^{5} + 6z^{5} – 6z^{4}; (–6z^{5}) + (–6z^{5}) + 6z^{4}

x – 1; 1 – x

(–5x^{2}) + (–2x) + (–10); 5x^{2} – 2x + 10
We will be using the additive inverse property to check all these polynomials.
Answer: Polynomials listed with their correct additive inverse are (a) x^{2} + 3x – 2; –x^{2} – 3x + 2, (c) 6z^{5} + 6z^{5} – 6z^{4}; (–6z^{5}) + (–6z^{5}) + 6z^{4}, and (d) x – 1; 1 – x.
Let's check these polynomials one by one.
Explanation:
Additive inverse means changing the sign of the number and adding it to the original number to get an answer equal to 0.
Example: Additive inverse of 7 is 7.
⇒ 7 + (7) = 0
Case 1:
Sum the polynomials = x^{2} + 3x – 2 –x^{2} – 3x + 2 = 0
They are additive inverses.
Case 2:
Sum the polynomials = –y^{7} – 10 –y^{7} + 10 = –2y^{7}
They are not additive inverses.
Case 3:
Sum the polynomials = 6z^{5} + 6z^{5} – 6z^{4} – 6z^{5} + (–6z^{5}) + 6z^{4} = 0
They are additive inverses.
Case 4:
Sum the polynomials = x – 1 + 1 – x = 0
They are additive inverses.
Case 5:
Sum the polynomials = (–5x^{2}) + (–2x) + (–10) + 5x^{2} – 2x + 10 = –4x
They are not additive inverses