completely factor the polynomial, if possible.

\x^2 + 4x + 16\

Question

completely factor the polynomial, if possible.

\x^2 + 4x + 16\

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", "Prime Polynomials" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Prime Polynomials" ] } ## Identify the polynomial form Using the *Factoring Trinomials* knowledge point $$ x^2 + 4x + 16 $$ ## Analyze factors of the constant term Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &\text{Factors of } 16: \ &1 \times 16 \implies 1 + 16 = 17 \ &2 \times 8 \implies 2 + 8 = 10 \ &4 \times 4 \implies 4 + 4 = 8 \end{aligned} $$ ## Check for prime status Using the *Prime Polynomials* knowledge point $$ \begin{aligned} &b^2 - 4ac = 4^2 - 4(1)(16) = 16 - 64 = -48 < 0 \ &\text{No real linear factors exist.} \end{aligned} $$ The polynomial is prime. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Prime Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the polynomial form

Analyze factors of the constant term

Check for prime status

Answer: