4. 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": [ "Algebraic Expression Simplification" ], "new_concepts": [ "Polynomial Simplification", "Combining Like Terms" ], "current_concepts": [ "Algebraic Expression Simplification", "Polynomial Simplification", "Combining Like Terms" ] } ## Identify the given expression The given algebraic expression to simplify is: $$ -4m^2 + 5m + 2m - 2m^3 + m^2 - 6 $$ ## Group the like terms Using the **Algebraic Expression Simplification** knowledge point $$ \begin{aligned} \text{Terms in } m^3: & \quad -2m^3 \ \text{Terms in } m^2: & \quad -4m^2 + m^2 \ \text{Terms in } m: & \quad 5m + 2m \ \text{Constant terms}: & \quad -6 \end{aligned} $$ ## Combine coefficients for each group We combine the coefficients of the like terms: $$ \begin{aligned} -2m^3 & = -2m^3 \ (-4 + 1)m^2 & = -3m^2 \ (5 + 2)m & = 7m \ -6 & = -6 \end{aligned} $$ ## Write the simplified polynomial We write the final simplified polynomial in standard form (descending order of powers): $$ -2m^3 - 3m^2 + 7m - 6 $$ $$-2m^3 - 3m^2 + 7m - 6$$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Simplification" ] }

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Question

Explanation:

Identify the given expression

Group the like terms

Combine coefficients for each group

Write the simplified polynomial

Answer: