completely factor the trinomial, if possible.

\12x^2 + 13x + 3\

Question

completely factor the trinomial, if possible.

\12x^2 + 13x + 3\

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", "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 Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &12x^2 + 13x + 3\ &a = 12,\quad b = 13,\quad c = 3 \end{aligned} $$ ## Find key factors Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &a \cdot c = 12 \cdot 3 = 36\ &p \cdot q = 36,\quad p + q = 13\ &p = 9,\quad q = 4 \end{aligned} $$ ## Rewrite middle term Using the *Trinomial Factoring by Grouping* knowledge point $$ 12x^2 + 9x + 4x + 3 $$ ## Factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &(12x^2 + 9x) + (4x + 3)\ &= 3x(4x + 3) + 1(4x + 3)\ &= (3x + 1)(4x + 3) \end{aligned} $$ Completely factor the trinomial, if possible. $12x^2 + 13x + 3 =$ $(3x + 1)(4x + 3)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients

Find key factors

Rewrite middle term

Factor by grouping

Answer: