match each polynomial expression to its additive inverse.

left options:
1. $-6x^2 - x - 2$
2. $-6x^2 + x - 2$
3. $6x^2 + x - 2$
4. $6x^2 - x + 2$

right options:
- $-6x^2 - x + 2$
- $-6x^2 + x - 2$
- $6x^2 + x + 2$
- $6x^2 - x + 2$

Question

match each polynomial expression to its additive inverse.

left options:
1. $-6x^2 - x - 2$
2. $-6x^2 + x - 2$
3. $6x^2 + x - 2$
4. $6x^2 - x + 2$

right options:
- $-6x^2 - x + 2$
- $-6x^2 + x - 2$
- $6x^2 + x + 2$
- $6x^2 - x + 2$

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Terms" ], "new_concepts": [ "Additive Inverse" ], "current_concepts": [ "Polynomial Terms", "Additive Inverse" ] } ## Define the additive inverse operation $$ -(ax^2 + bx + c) = -ax^2 - bx - c $$ ## Calculate the additive inverse for each expression $$ \begin{aligned} &-(-6x^2 - x - 2) = 6x^2 + x + 2 \ &-(-6x^2 + x - 2) = 6x^2 - x + 2 \ &-(6x^2 + x - 2) = -6x^2 - x + 2 \ &-(6x^2 - x + 2) = -6x^2 + x - 2 \end{aligned} $$ ## Match each expression to the corresponding option $$ \begin{aligned} &-6x^2 - x - 2 \longrightarrow 6x^2 + x + 2 \ &-6x^2 + x - 2 \longrightarrow 6x^2 - x + 2 \ &6x^2 + x - 2 \longrightarrow -6x^2 - x + 2 \ &6x^2 - x + 2 \longrightarrow -6x^2 + x - 2 \end{aligned} $$ | Polynomial Expression | Additive Inverse | |---|---| | $-6x^2 - x - 2$ | $6x^2 + x + 2$ | | $-6x^2 + x - 2$ | $6x^2 - x + 2$ | | $6x^2 + x - 2$ | $-6x^2 - x + 2$ | | $6x^2 - x + 2$ | $-6x^2 + x - 2$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Additive Inverse" ] }

Polynomial Expression	Additive Inverse
\(-6x^2 + x - 2\)	\(6x^2 - x + 2\)
\(6x^2 + x - 2\)	\(-6x^2 - x + 2\)
\(6x^2 - x + 2\)	\(-6x^2 + x - 2\)

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QUESTION IMAGE

Question

Explanation:

Define the additive inverse operation

Calculate the additive inverse for each expression

Match each expression to the corresponding option

Answer: