solve.

\3m^3 + 18m^2 - 48m = 0\

Question

solve.

\3m^3 + 18m^2 - 48m = 0\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Zero Product Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Solving Quadratic Equations", "Polynomial Factoring" ] } ## Factor out the greatest common factor $$ 3m(m^2 + 6m - 16) = 0 $$ ## Factor the quadratic trinomial $$ 3m(m + 8)(m - 2) = 0 $$ ## Apply the zero product property to solve for m $$ \begin{aligned} 3m = 0 &\implies m = 0 \ m + 8 = 0 &\implies m = -8 \ m - 2 = 0 &\implies m = 2 \end{aligned} $$ Solve. $$3m^3 + 18m^2 - 48m = 0$$ $m = 0, -8, 2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the quadratic trinomial

Apply the zero product property to solve for m

Answer: