completely factor the trinomial, if possible.

\6b^2 + 11b + 3\

Question

completely factor the trinomial, if possible.

\6b^2 + 11b + 3\

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 coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &6b^2 + 11b + 3\ &a = 6,\quad b = 11,\quad c = 3 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (ac) = 6 \times 3 = 18\ &\text{Sum } (b) = 11\ &\text{Factors of 18 that sum to 11: } 2 \text{ and } 9 \end{aligned} $$ ## Rewrite the middle term Using the *Trinomial Factoring by Grouping* knowledge point $$ 6b^2 + 2b + 9b + 3 $$ ## Factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &2b(3b + 1) + 3(3b + 1)\ &(2b + 3)(3b + 1) \end{aligned} $$ $(2b + 3)(3b + 1)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the trinomial

Find factors with given sum and product

Rewrite the middle term

Factor by grouping

Answer: