completely factor the trinomial, if possible.

\6y^2 + 31y + 5\

Question

completely factor the trinomial, if possible.

\6y^2 + 31y + 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", "Trinomial Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Trinomial Factoring by Grouping" ] } ## Identify the coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &6y^2 + 31y + 5\ &a = 6,\quad b = 31,\quad c = 5 \end{aligned} $$ ## Find two numbers with a given product and sum Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &ac = 6 \times 5 = 30\ &b = 31\ &\text{Factors: } 30 \text{ and } 1 \quad (30 \times 1 = 30,\ 30 + 1 = 31) \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &6y^2 + 30y + y + 5\ &= 6y(y + 5) + 1(y + 5)\ &= (6y + 1)(y + 5) \end{aligned} $$ $(6y + 1)(y + 5)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the trinomial

Find two numbers with a given product and sum

Rewrite the middle term and factor by grouping

Answer: