what is the factored form of (x^2 - x - 2)?

* ((x - 2)(x + 1))
* ((x + 2)(x + 1))
* ((x - 2)(x - 1))
* ((x + 2)(x - 1))

Question

what is the factored form of (x^2 - x - 2)?

* ((x - 2)(x + 1))
* ((x + 2)(x + 1))
* ((x - 2)(x - 1))
* ((x + 2)(x - 1))

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

(A) $(x - 2)(x + 1)$

(B) $(x + 2)(x + 1)$

(C) $(x - 2)(x - 1)$

(D) $(x + 2)(x - 1)$

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

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Question

Explanation:

Identify the coefficients of the quadratic expression

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

Write the expression in factored form

Answer: