al, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\2x^2 - 17x + 21\

not factorable

Question

al, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\2x^2 - 17x + 21\

not factorable

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 Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 2x^2 - 17x + 21\ &a = 2,\quad b = -17,\quad c = 21 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product } (ac) = 2 \times 21 = 42\ &\text{Sum } (b) = -17\ &\text{Factors of } 42 \text{ that sum to } -17: -3 \text{ and } -14\ &(-3) \times (-14) = 42\ &(-3) + (-14) = -17 \end{aligned} $$ ## Rewrite and group the terms Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &2x^2 - 17x + 21 = 2x^2 - 14x - 3x + 21\ &\text{Group terms: } (2x^2 - 14x) - (3x - 21) \end{aligned} $$ ## Factor out the common terms Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &2x(x - 7) - 3(x - 7)\ &(2x - 3)(x - 7) \end{aligned} $$ $(2x - 3)(x - 7)$ { "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

Rewrite and group the terms

Factor out the common terms

Answer: