completely factor the trinomial, if possible.

\6b^2 + 43b + 7\

Question

completely factor the trinomial, if possible.

\6b^2 + 43b + 7\

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 $$ \begin{aligned} &6b^2 + 43b + 7\ &a = 6,\quad b = 43,\quad c = 7 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &ac = 6 \times 7 = 42\ &\text{Sum} = 43\ &\text{Factors: } 42 \text{ and } 1 \quad (42 \times 1 = 42,\ 42 + 1 = 43) \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &6b^2 + 42b + b + 7\ &= 6b(b + 7) + 1(b + 7)\ &= (6b + 1)(b + 7) \end{aligned} $$ $(6b + 1)(b + 7)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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Question

Explanation:

Identify the coefficients of the trinomial

Find two numbers that multiply to ac and add to b

Rewrite the middle term and factor by grouping

Answer: