completely factor the given polynomial. if a polynomial cannot be factored, enter
f\.

\20n^2 + 80n - 70\

Question

completely factor the given polynomial. if a polynomial cannot be factored, enter
f\.

\20n^2 + 80n - 70\

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" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ] } ## Find the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &\text{Terms: } 20n^2, \quad 80n, \quad -70\ &\text{GCF}(20, 80, 70) = 10\ &20n^2 + 80n - 70 = 10(2n^2 + 8n - 7) \end{aligned} $$ ## Analyze the remaining trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &\text{Trinomial: } 2n^2 + 8n - 7\ &a = 2, \quad b = 8, \quad c = -7\ &ac = 2 \times (-7) = -14\ &\text{Factors of } -14 \text{ that sum to } 8: \text{None exist}\ &\text{The trinomial } 2n^2 + 8n - 7 \text{ is prime.} \end{aligned} $$ Completely factor the given polynomial. If a polynomial cannot be factored, enter "NF". $20n^2 + 80n - 70 =$ $10(2n^2 + 8n - 7)$ { "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

Analyze the remaining trinomial

Answer: