completely factor the given trinomial.

\39x^2 - 19x + 2\

Question

completely factor the given trinomial.

\39x^2 - 19x + 2\

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", "Finding Factors with Given Sum and Product", "Trinomial Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product", "Trinomial Factoring by Grouping" ] } ## Identify coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 39x^2 - 19x + 2\ &a = 39,\quad b = -19,\quad c = 2 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (ac) = 39 \times 2 = 78\ &\text{Sum } (b) = -19\ &\text{Factors: } -13 \text{ and } -6 \quad [(-13) \times (-6) = 78, \ (-13) + (-6) = -19] \end{aligned} $$ ## Rewrite and group the terms Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &39x^2 - 19x + 2 = 39x^2 - 13x - 6x + 2\ &=(39x^2 - 13x) - (6x - 2) \end{aligned} $$ ## Factor out the greatest common factor from each group Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} &13x(3x - 1) - 2(3x - 1) \end{aligned} $$ ## Factor out the common binomial Using the *Factoring by Grouping* knowledge point $$ \begin{aligned} &(3x - 1)(13x - 2) \end{aligned} $$ Completely factor the given trinomial. $(3x - 1)(13x - 2)$ { "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 group the terms

Factor out the greatest common factor from each group

Factor out the common binomial

Answer: