completely factor the trinomial, if possible.

\2x^2 + 11x - 21\

Question

completely factor the trinomial, if possible.

\2x^2 + 11x - 21\

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 $$ \begin{aligned} &2x^2 + 11x - 21\ &a = 2,\quad b = 11,\quad c = -21 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a \cdot c = 2 \cdot (-21) = -42\ &b = 11\ &\text{Factors of } -42 \text{ that sum to } 11 \text{ are } 14 \text{ and } -3\ &14 \cdot (-3) = -42\ &14 + (-3) = 11 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &2x^2 + 11x - 21 = 2x^2 + 14x - 3x - 21\ &2x^2 + 14x - 3x - 21 = (2x^2 + 14x) - (3x + 21)\ &2x(x + 7) - 3(x + 7)\ &(2x - 3)(x + 7) \end{aligned} $$ $(2x - 3)(x + 7)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

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: