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

\q^2 + 4q - 8\

Question

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

\q^2 + 4q - 8\

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 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 $$ \begin{aligned} &q^2 + 4q - 8\ &a = 1,\quad b = 4,\quad c = -8 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product} = a \cdot c = 1 \cdot (-8) = -8\ &\text{Sum} = b = 4 \end{aligned} $$ ## Test integer factor pairs of -8 Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &1 \cdot (-8) = -8 \implies 1 + (-8) = -7 e 4\ &-1 \cdot 8 = -8 \implies -1 + 8 = 7 e 4\ &2 \cdot (-4) = -8 \implies 2 + (-4) = -2 e 4\ &-2 \cdot 4 = -8 \implies -2 + 4 = 2 e 4 \end{aligned} $$ ## Determine factorability Using the *Factoring Trinomials* knowledge point $$ \text{No integer pairs multiply to } -8 \text{ and sum to } 4. $$ Factor the trinomial. If the trinomial cannot be factored, indicate "Not Factorable". $$q^2 + 4q - 8$$ Not Factorable { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "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

Test integer factor pairs of -8

Determine factorability

Answer: