completely factor the given trinomial.

\33x^2 - 17x + 2\

Question

completely factor the given trinomial.

\33x^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", "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 the coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 33x^2 - 17x + 2\ &a = 33,\quad b = -17,\quad c = 2 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (ac) = 33 \times 2 = 66\ &\text{Sum } (b) = -17\ &\text{Factors: } -11 \text{ and } -6\ &(-11) \times (-6) = 66\ &(-11) + (-6) = -17 \end{aligned} $$ ## Split the middle term Using the *Trinomial Factoring by Grouping* knowledge point $$ 33x^2 - 11x - 6x + 2 $$ ## Factor by grouping Using the *Factoring Polynomials by GCF* and *Factoring by Grouping* knowledge points $$ \begin{aligned} &(33x^2 - 11x) - (6x - 2)\ &= 11x(3x - 1) - 2(3x - 1)\ &= (11x - 2)(3x - 1) \end{aligned} $$ $(11x - 2)(3x - 1)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Find factors with given sum and product

Split the middle term

Factor by grouping

Answer: