completely factor the trinomial, if possible.

\x^2 - 12x + 32\

Question

completely factor the trinomial, if possible.

\x^2 - 12x + 32\

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" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ] } ## Identify the trinomial coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &x^2 - 12x + 32\ &a = 1,\quad b = -12,\quad c = 32 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &p \cdot q = 32\ &p + q = -12\ &p = -4,\quad q = -8 \end{aligned} $$ ## Write the factored form Using the *Factoring Trinomials* knowledge point $$ (x - 4)(x - 8) $$ Completely factor the trinomial, if possible. $x^2 - 12x + 32 =$ $(x - 4)(x - 8)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the trinomial coefficients

Find factors with given sum and product

Write the factored form

Answer: