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))

Explanation:

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<reasoning>

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

\[
x^2 - x - 2 = (x - 2)(x + 1)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((x - 2)(x + 1)\)</mcq-correct>
<mcq-option>(B) \((x + 2)(x + 1)\)</mcq-option>
<mcq-option>(C) \((x - 2)(x - 1)\)</mcq-option>
<mcq-option>(D) \((x + 2)(x - 1)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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

\[
x^2 - x - 2 = (x - 2)(x + 1)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((x - 2)(x + 1)\)</mcq-correct>
<mcq-option>(B) \((x + 2)(x + 1)\)</mcq-option>
<mcq-option>(C) \((x - 2)(x - 1)\)</mcq-option>
<mcq-option>(D) \((x + 2)(x - 1)\)</mcq-option>
</answer>

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