what is the factored form of the polynomial?

(x^2 - 12x + 27)?

( ) ((x + 4)(x + 3))
( ) ((x - 4)(x + 3))
( ) ((x + 9)(x + 3))
( ) ((x - 9)(x - 3))

Question

what is the factored form of the polynomial?

(x^2 - 12x + 27)?

( ) ((x + 4)(x + 3))
( ) ((x - 4)(x + 3))
( ) ((x + 9)(x + 3))
( ) ((x - 9)(x - 3))

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" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Polynomial Operations" ] } ## Identify the coefficients of the quadratic trinomial $$ a = 1, \quad b = -12, \quad c = 27 $$ ## Find two numbers that multiply to $c$ and add to $b$ $$ \begin{aligned} &p \cdot q = 27\ &p + q = -12\ &\Rightarrow p = -9, \quad q = -3 \end{aligned} $$ ## Write the trinomial in its factored form $$ x^2 - 12x + 27 = (x - 9)(x - 3) $$

(A) $(x + 4)(x + 3)$

(B) $(x - 4)(x + 3)$

(C) $(x + 9)(x + 3)$

(D) $(x - 9)(x - 3)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic trinomial

Find two numbers that multiply to \(c\) and add to \(b\)

Write the trinomial in its factored form

Answer: