solve the following equation by factoring. separate multiple answers with a comma.

\x^3 - 45x = 4x^2\

Question

solve the following equation by factoring. separate multiple answers with a comma.

\x^3 - 45x = 4x^2\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Factoring Trinomials", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials", "Zero Product Property" ] } ## Rearrange the equation into standard form Using the **Polynomial Subtraction** knowledge point $$ \begin{aligned} &x^3 - 45x = 4x^2\ &x^3 - 4x^2 - 45x = 0 \end{aligned} $$ ## Factor out the greatest common factor Using the **Factoring Polynomials by GCF** knowledge point $$ \begin{aligned} &x(x^2 - 4x - 45) = 0 \end{aligned} $$ ## Factor the quadratic trinomial Using the **Factoring Trinomials** knowledge point $$ \begin{aligned} &x^2 - 4x - 45 = (x - 9)(x + 5)\ &x(x - 9)(x + 5) = 0 \end{aligned} $$ ## Apply the zero product property to find all roots Using the **Zero Product Property** knowledge point $$ \begin{aligned} &x = 0 \quad\text{or}\quad x - 9 = 0 \quad\text{or}\quad x + 5 = 0\ &x = 0, \quad x = 9, \quad x = -5 \end{aligned} $$ Solve the following equation by factoring. Separate multiple answers with a comma. $x^3 - 45x = 4x^2$ $0, 9, -5$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the equation into standard form

Factor out the greatest common factor

Factor the quadratic trinomial

Apply the zero product property to find all roots

Answer: