Which polynomials are listed with their correct additive inverse? Check all that apply.
x² + 3x - 2; -x² - 3x + 2
-y⁷ - 10; -y⁷ + 10
6z⁵ + 6z⁵ - 6z⁴; (-6z⁵) + (-6z⁵) + 6z⁴
x - 1; 1 - x
(-5x²) + (-2x) + (-10); 5x² - 2x + 10

Solution:

We will be using the additive inverse property to check all these polynomials.

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 = x² + 3x - 2 - x² - 3x + 2 = 0

They are additive inverses.

Case 2:

Sum the polynomials = -y⁷ - 10 - y⁷ + 10 = -2y⁷

They are not additive inverses.

Case 3:

Sum the polynomials = 6z⁵ + 6z⁵ - 6z⁴ - 6z⁵ + (-6z⁵) + 6z⁴ = 0

They are additive inverses.

Case 4:

Sum the polynomials = x - 1 + 1 - x = 0

They are additive inverses.

Case 5:

Sum the polynomials = (-5x²) + (-2x) + (-10) + 5x² - 2x + 10 = -4x

They are not additive inverses

Hence, polynomials x² + 3x - 2; -x² - 3x + 2, 6z⁵ + 6z⁵ - 6z⁴; (-6z⁵) + (-6z⁵) + 6z⁴, and x - 1; 1 - x are listed with their correct additive inverse.

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

Summary:

Polynomials listed with their correct additive inverse are (a) x² + 3x - 2; -x² - 3x + 2, (c) 6z⁵ + 6z⁵ – 6z⁴; (-6z⁵) + (-6z⁵) + 6z⁴, and (d) x - 1; 1 - x.