completely factor the given polynomial. if the polynomial cannot be factored, write nf for your answer.

\96x^3 - 54x\

Question

completely factor the given polynomial. if the polynomial cannot be factored, write nf for your answer.

\96x^3 - 54x\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Difference of Squares" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Difference of Squares" ] } ## Identify the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &\text{Terms: } 96x^3, \quad -54x\ &\text{GCF of } 96 \text{ and } 54 = 6\ &\text{GCF of } x^3 \text{ and } x = x\ &\text{Overall GCF} = 6x \end{aligned} $$ ## Factor out the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ 96x^3 - 54x = 6x(16x^2 - 9) $$ ## Factor the remaining binomial Using the *Difference of Squares* knowledge point $$ \begin{aligned} &16x^2 - 9 = (4x)^2 - 3^2\ &(4x)^2 - 3^2 = (4x - 3)(4x + 3) \end{aligned} $$ ## Combine all factors Using the *Factoring Polynomials by GCF* and *Difference of Squares* knowledge points $$ 96x^3 - 54x = 6x(4x - 3)(4x + 3) $$ $6x(4x - 3)(4x + 3)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials by GCF" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the greatest common factor

Factor out the greatest common factor

Factor the remaining binomial

Combine all factors

Answer: