the trinomial, if possible.

\6x^2 + 2x - 28\

Question

the trinomial, if possible.

\6x^2 + 2x - 28\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Factoring Trinomials", "Trinomial Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials", "Trinomial Factoring by Grouping" ] } ## Factor out the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ 6x^2 + 2x - 28 = 2(3x^2 + x - 14) $$ ## Find factors for grouping Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a = 3,\quad b = 1,\quad c = -14\ &a \cdot c = 3 \cdot (-14) = -42\ &\text{Factors of } -42 \text{ that sum to } 1: 7 \text{ and } -6 \end{aligned} $$ ## Rewrite and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} 3x^2 + x - 14 &= 3x^2 - 6x + 7x - 14\ &= 3x(x - 2) + 7(x - 2)\ &= (3x + 7)(x - 2) \end{aligned} $$ ## Write the complete factored expression Combine the greatest common factor with the factored trinomial: $$ 2(3x + 7)(x - 2) $$ $2(3x + 7)(x - 2)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Find factors for grouping

Rewrite and factor by grouping

Write the complete factored expression

Answer: