Question

what is the additive inverse of the polynomial?

(-6x^3 + 4x^2 - 4x)

• (6x^3 + 4x^2 + 4x)
• (6x^3 - 4x^2 + 4x)
• (-6x^3 - 4x^2 - 4x)
• (6x^3 + 4x^2 - 4x)

Explanation:

🆕 New Concept Discovered: Additive Inverse of a Polynomial
Opposite signs for every term

Step 1: Understand additive inverse

The additive inverse of any expression is what you add to it to get a sum of \( 0 \). In practice, this means you change the sign of every single term in the expression (multiply the entire expression by \( -1 \)).

$$ -(-6x^3 + 4x^2 - 4x) $$

Step 2: Distribute the negative sign

Distribute the negative sign to each term inside the parentheses:

$$ -(-6x^3) - (4x^2) - (-4x) $$

This simplifies to:

$$ 6x^3 - 4x^2 + 4x $$

Answer:

\( 6x^3 - 4x^2 + 4x \) (the second option)