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

\98x^3 - 72x\

Question

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

\98x^3 - 72x\

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" ] } ## Find the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &\text{Terms: } 98x^3, \quad -72x\ &\text{GCF of } 98 \text{ and } 72: \quad \gcd(98, 72) = 2\ &\text{GCF of } x^3 \text{ and } x: \quad x\ &\text{Overall GCF: } 2x\ &98x^3 - 72x = 2x(49x^2 - 36) \end{aligned} $$ ## Factor the remaining binomial Using the *Difference of Squares* knowledge point $$ \begin{aligned} &49x^2 - 36 = (7x)^2 - 6^2\ &(7x)^2 - 6^2 = (7x - 6)(7x + 6)\ &98x^3 - 72x = 2x(7x - 6)(7x + 6) \end{aligned} $$ $2x(7x - 6)(7x + 6)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials by GCF" ] }

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QUESTION IMAGE

Question

Explanation:

Find the greatest common factor

Factor the remaining binomial

Answer: