simplify each polynomial (2 marks)
a) $-4m^2 + 5m + 2m - 2m^3 + m^2 - 6$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Polynomial Simplification", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Simplification", "Combining Like Terms" ] } ## Identify the terms of the polynomial To simplify the expression, we first list all the individual terms in the given polynomial: $$-4m^2 + 5m + 2m - 2m^3 + m^2 - 6$$ ## Group the like terms Using the **Polynomial Simplification** knowledge point $$ \begin{aligned} &\text{Terms with } m^3: -2m^3\ &\text{Terms with } m^2: -4m^2, m^2\ &\text{Terms with } m: 5m, 2m\ &\text{Constant terms}: -6 \end{aligned} $$ ## Combine the like terms Using the **Combining Like Terms** knowledge point $$ \begin{aligned} &-2m^3 + (-4m^2 + m^2) + (5m + 2m) - 6\ &= -2m^3 - 3m^2 + 7m - 6 \end{aligned} $$ $-2m^3 - 3m^2 + 7m - 6$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Simplification" ] }

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Explanation:

Identify the terms of the polynomial

Group the like terms

Combine the like terms

Answer: