select the correct answer.

what is the factored form of this expression?

(x^2 - 12x + 36)

((x - 12)(x - 3))

((x - 6)(x + 6))

((x - 6)^2)

((x + 6)^2)

Question

select the correct answer.

what is the factored form of this expression?

(x^2 - 12x + 36)

((x - 12)(x - 3))

((x - 6)(x + 6))

((x - 6)^2)

((x + 6)^2)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Perfect Square Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Perfect Square Trinomials" ] } ## Identify the trinomial structure $$ x^2 - 12x + 36 $$ ## Apply the perfect square trinomial pattern $$ \begin{aligned} a^2 - 2ab + b^2 &= (a - b)^2 \ x^2 - 2(x)(6) + 6^2 &= (x - 6)^2 \end{aligned} $$ ## Verify the factored form $$ (x - 6)^2 = (x - 6)(x - 6) = x^2 - 12x + 36 $$

(x - 12)(x - 3)

(x - 6)(x + 6)

(x - 6)^2

(x + 6)^2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect Square Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the trinomial structure

Apply the perfect square trinomial pattern

Verify the factored form

Answer: