Question

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\\)

Explanation:

Define the additive inverse of a polynomial

$$ P(x) + Q(x) = 0 \implies Q(x) = -P(x) $$

Evaluate each option by negating the first polynomial

$$
LATEXBLOCK0
$$

Identify the correct options

$$ \text{Options 1, 3, and 4 are correct.} $$

Answer:

• (A) \(x^2 + 3x - 2;\ -x^2 - 3x + 2\) (Correct answer)
• (B) \(-y^7 - 10;\ -y^7 + 10\)
• (C) \(6z^5 + 6z^5 - 6z^4;\ (-6z^5) + (-6z^5) + 6z^4\) (Correct answer)
• (D) \(x - 1;\ 1 - x\) (Correct answer)
• (E) \((-5x^2) + (-2x) + (-10);\ 5x^2 - 2x + 10\)