solve:
\0 = -5x^6 + 115x^5 - 660x^4\
\x = \

Question

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" ], "new_concepts": [ "Polynomial Factoring", "Higher Degree Equations" ], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Polynomial Factoring", "Higher Degree Equations" ] } ## Factor out the greatest common factor $$ 0 = -5x^4(x^2 - 23x + 132) $$ ## Factor the quadratic trinomial $$ 0 = -5x^4(x - 11)(x - 12) $$ ## Apply the zero product property to find all roots $$ x = 0, \quad x = 11, \quad x = 12 $$ Solve: $$0 = -5x^6 + 115x^5 - 660x^4$$ $x =$ $0, 11, 12$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the quadratic trinomial

Apply the zero product property to find all roots

Answer: