factor the given trinomial. if the trinomial cannot be factored, indicate
ot factorable\.

\v^2 - 7v + 14\

Question

factor the given trinomial. if the trinomial cannot be factored, indicate
ot factorable\.

\v^2 - 7v + 14\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ] } ## Identify the trinomial coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &v^2 - 7v + 14\ &a = 1,\quad b = -7,\quad c = 14 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product} = 14\ &\text{Sum} = -7\ &\text{Factor pairs of } 14: (-1, -14), (-2, -7)\ &\text{Sums: } -15, -9 e -7 \end{aligned} $$ ## Determine factorability Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &b^2 - 4ac = (-7)^2 - 4(1)(14) = 49 - 56 = -7 < 0\ &\text{No integer factors exist.} \end{aligned} $$

Factor the trinomial

Not Factorable

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the trinomial coefficients

Find factors with given sum and product

Determine factorability

Answer: