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

\x^2 - 4x - 5\

Question

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

\x^2 - 4x - 5\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "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 $$ \begin{aligned} &x^2 - 4x - 5\ &a = 1,\quad b = -4,\quad c = -5 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product} = a \cdot c = 1 \cdot (-5) = -5\ &\text{Sum} = b = -4\ &\text{Factors: } -5 \text{ and } 1\ &(-5) \cdot 1 = -5\ &(-5) + 1 = -4 \end{aligned} $$ ## Write the factored form Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &x^2 - 4x - 5 = (x - 5)(x + 1) \end{aligned} $$ $(x - 5)(x + 1)$ { "subject": "Mathematics", "question_type": "Free Response", "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

Write the factored form

Answer: