completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\x^2 - 3x - 18\

Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\x^2 - 3x - 18\

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" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ] } ## Identify the trinomial coefficients Using the **Factoring Trinomials** knowledge point $$ \begin{aligned} &x^2 - 3x - 18\ &a = 1,\quad b = -3,\quad c = -18 \end{aligned} $$ ## Find factors with given sum and product Using the **Finding Factors with Given Sum and Product** knowledge point $$ \begin{aligned} &\text{Product} = a \cdot c = -18\ &\text{Sum} = b = -3\ &\text{Factors: } 3 \text{ and } -6\ &3 \cdot (-6) = -18\ &3 + (-6) = -3 \end{aligned} $$ ## Write the factored form Using the **Factoring Trinomials** knowledge point $$ \begin{aligned} &x^2 - 3x - 18 = (x + 3)(x - 6) \end{aligned} $$ $(x + 3)(x - 6)$ { "subject": "Mathematics", "question_type": "Free Response", "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: