the factors of $x^2 - 3x - 18$ are

a $(x - 6), (x + 3)$

b $(x + 6), (x - 3)$

c $(x - 9), (x + 2)$

d $(x + 9), (x - 2)$

Question

the factors of $x^2 - 3x - 18$ are

a $(x - 6), (x + 3)$

b $(x + 6), (x - 3)$

c $(x - 9), (x + 2)$

d $(x + 9), (x - 2)$

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", "Quadratic Factoring" ], "current_concepts": [ "Factoring Trinomials", "Quadratic Factoring" ] } ## Identify coefficients of the quadratic expression $$ \begin{aligned} &x^2 - 3x - 18\ &a = 1,\quad b = -3,\quad c = -18 \end{aligned} $$ ## Find two numbers that multiply to $c$ and add to $b$ $$ \begin{aligned} &p \cdot q = -18\ &p + q = -3\ &p = -6,\quad q = 3 \end{aligned} $$ ## Write the expression in factored form $$ x^2 - 3x - 18 = (x - 6)(x + 3) $$

(A) $(x - 6), (x + 3)$

(B) $(x + 6), (x - 3)$

(C) $(x - 9), (x + 2)$

(D) $(x + 9), (x - 2)$

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

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Question

Explanation:

Identify coefficients of the quadratic expression

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

Write the expression in factored form

Answer: