which shows the factored form of (x^2 - 12x - 45)?

(x + 3)(x - 15)
(x - 3)(x - 15)
(x + 3)(x + 15)
(x - 3)(x + 15)

Question

which shows the factored form of (x^2 - 12x - 45)?

(x + 3)(x - 15)
(x - 3)(x - 15)
(x + 3)(x + 15)
(x - 3)(x + 15)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Factoring Trinomials" ], "current_concepts": [ "Factoring Trinomials", "Trinomial Coefficients", "Factoring Signs" ] } ## Identify the coefficients of the quadratic expression $$ \begin{aligned} &a = 1\ &b = -12\ &c = -45 \end{aligned} $$ ## Find two numbers that multiply to c and add to b $$ \begin{aligned} &p \cdot q = -45\ &p + q = -12\ &\text{Factors of } -45: \quad 3 \text{ and } -15\ &3 \cdot (-15) = -45\ &3 + (-15) = -12 \end{aligned} $$ ## Write the expression in factored form $$ x^2 - 12x - 45 = (x + 3)(x - 15) $$

(x + 3)(x - 15)

(x - 3)(x - 15)

(x + 3)(x + 15)

(x - 3)(x + 15)

{ "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 expression

Find two numbers that multiply to c and add to b

Write the expression in factored form

Answer: