completely factor the trinomial, if possible.

\6x^2 + 11x - 2\

Question

completely factor the trinomial, if possible.

\6x^2 + 11x - 2\

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", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ] } ## Identify coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a = 6\ &b = 11\ &c = -2 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (a \cdot c) = 6 \cdot (-2) = -12\ &\text{Sum } (b) = 11\ &\text{Factors of } -12 \text{ that sum to } 11: 12 \text{ and } -1 \end{aligned} $$ ## Rewrite and group the terms Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} 6x^2 + 11x - 2 &= 6x^2 + 12x - x - 2\ &= 6x(x + 2) - 1(x + 2) \end{aligned} $$ ## Factor out the common binomial Using the *Factoring Trinomials* knowledge point $$ (6x - 1)(x + 2) $$ Completely factor the trinomial, if possible. $6x^2 + 11x - 2 =$ $(6x - 1)(x + 2)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "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 and group the terms

Factor out the common binomial

Answer: