completely factor the trinomial, if possible.

\7v^2 + 37v + 10\

Question

completely factor the trinomial, if possible.

\7v^2 + 37v + 10\

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 of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &7v^2 + 37v + 10\ &a = 7,\quad b = 37,\quad c = 10 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &P = a \cdot c = 7 \cdot 10 = 70\ &S = b = 37\ &\text{Factors: } 35 \text{ and } 2 \quad (35 \cdot 2 = 70,\quad 35 + 2 = 37) \end{aligned} $$ ## Rewrite and factor by grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &7v^2 + 35v + 2v + 10\ &= 7v(v + 5) + 2(v + 5)\ &= (7v + 2)(v + 5) \end{aligned} $$ Completely factor the trinomial, if possible. $7v^2 + 37v + 10 =$ $(7v + 2)(v + 5)$ { "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 factor by grouping

Answer: