completely factor the given trinomial.

\26x^2 - 17x + 2\

Question

completely factor the given trinomial.

\26x^2 - 17x + 2\

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", "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 the coefficients of the trinomial Using the **Factoring Trinomials** knowledge point $$ \begin{aligned} &ax^2 + bx + c = 26x^2 - 17x + 2\ &a = 26,\quad b = -17,\quad c = 2 \end{aligned} $$ ## Find two numbers with a given sum and product Using the **Finding Factors with Given Sum and Product** knowledge point $$ \begin{aligned} &\text{Product } (ac) = 26 \times 2 = 52\ &\text{Sum } (b) = -17\ &\text{Factors: } -13 \text{ and } -4 \quad (\text{since } -13 \times -4 = 52 \text{ and } -13 + (-4) = -17) \end{aligned} $$ ## Rewrite and factor the trinomial by grouping Using the **Trinomial Factoring by Grouping** knowledge point $$ \begin{aligned} 26x^2 - 17x + 2 &= 26x^2 - 13x - 4x + 2\ &= 13x(2x - 1) - 2(2x - 1)\ &= (2x - 1)(13x - 2) \end{aligned} $$ $(2x - 1)(13x - 2)$ { "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 with a given sum and product

Rewrite and factor the trinomial by grouping

Answer: