completely factor the trinomial, if possible.

\3c^2 + 10c - 8\

Question

completely factor the trinomial, if possible.

\3c^2 + 10c - 8\

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", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ] } ## Identify the coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &3c^2 + 10c - 8\ &a = 3,\quad b = 10,\quad c = -8 \end{aligned} $$ ## Find factors for grouping Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product: } a \cdot c = 3 \cdot (-8) = -24\ &\text{Sum: } b = 10\ &\text{Factors: } 12 \text{ and } -2 \end{aligned} $$ ## Rewrite the middle term Using the *Trinomial Factoring by Grouping* knowledge point $$ 3c^2 + 12c - 2c - 8 $$ ## Factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &3c(c + 4) - 2(c + 4)\ &(3c - 2)(c + 4) \end{aligned} $$ $(3c - 2)(c + 4)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Find factors for grouping

Rewrite the middle term

Factor by grouping

Answer: