completely factor the trinomial, if possible.

\8t^2 + 10t - 7\

Question

completely factor the trinomial, if possible.

\8t^2 + 10t - 7\

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 coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &8t^2 + 10t - 7\ &a = 8,\quad b = 10,\quad c = -7 \end{aligned} $$ ## Find factors with given product and sum Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &ac = 8 \times (-7) = -56\ &b = 10\ &\text{Factors: } 14 \text{ and } -4 \quad (14 \times (-4) = -56, \quad 14 + (-4) = 10) \end{aligned} $$ ## Rewrite and group the terms Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &8t^2 + 10t - 7 = 8t^2 - 4t + 14t - 7\ &\text{Grouped: } (8t^2 - 4t) + (14t - 7) \end{aligned} $$ ## Factor out the greatest common factor from each group Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &4t(2t - 1) + 7(2t - 1) \end{aligned} $$ ## Factor out the common binomial Using the *Factoring by Grouping* knowledge point $$ \begin{aligned} &(2t - 1)(4t + 7) \end{aligned} $$ $(2t - 1)(4t + 7)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the trinomial

Find factors with given product and sum

Rewrite and group the terms

Factor out the greatest common factor from each group

Factor out the common binomial

Answer: