out the gcf
\10x^3 - 14x^2 - 6x\

Question

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": [ "Greatest Common Factor", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Polynomial Factoring" ] } ## Find the GCF of the coefficients Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Coefficients: } 10, -14, -6\ &\text{Factors of } 10: 1, 2, 5, 10\ &\text{Factors of } 14: 1, 2, 7, 14\ &\text{Factors of } 6: 1, 2, 3, 6\ &\text{GCF}(10, 14, 6) = 2 \end{aligned} $$ ## Find the GCF of the variable terms Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Variable terms: } x^3, x^2, x\ &\text{Lowest power of } x: x^1\ &\text{GCF}(x^3, x^2, x) = x \end{aligned} $$ ## Combine to find the overall GCF Using the *Greatest Common Factor* knowledge point $$ \text{GCF} = 2x $$ ## Factor out the GCF from the polynomial Using the *Polynomial Factoring* knowledge point $$ \begin{aligned} &10x^3 - 14x^2 - 6x = 2x(5x^2 - 7x - 3) \end{aligned} $$ Factor out the GCF: $10x^3 - 14x^2 - 6x =$ $2x(5x^2 - 7x - 3)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Find the GCF of the coefficients

Find the GCF of the variable terms

Combine to find the overall GCF

Factor out the GCF from the polynomial

Answer: