completely factor the polynomial, if possible.

\9 + 6x + x^2\

Question

completely factor the polynomial, if possible.

\9 + 6x + x^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", "Square of a Binomial Sum" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Square of a Binomial Sum", "Perfect Square Trinomials" ] } ## Rearrange the polynomial terms Using the *Factoring Trinomials* knowledge point $$ x^2 + 6x + 9 $$ ## Identify the perfect square pattern Using the *Square of a Binomial Sum* knowledge point $$ \begin{aligned} &a^2 = x^2 \implies a = x\ &b^2 = 9 \implies b = 3\ &2ab = 2(x)(3) = 6x \end{aligned} $$ ## Factor using the binomial square formula Using the *Square of a Binomial Sum* knowledge point $$ (x + 3)^2 $$ $(x + 3)^2$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Rearrange the polynomial terms

Identify the perfect square pattern

Factor using the binomial square formula

Answer: