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)\\)

Explanation:

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<reasoning>

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

\[
x^2 - 3x - 18 = (x - 6)(x + 3)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((x - 6), (x + 3)\)</mcq-correct>
<mcq-option>(B) \((x + 6), (x - 3)\)</mcq-option>
<mcq-option>(C) \((x - 9), (x + 2)\)</mcq-option>
<mcq-option>(D) \((x + 9), (x - 2)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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

\[
x^2 - 3x - 18 = (x - 6)(x + 3)
\]
</reasoning>

<answer>
<mcq-correct>(A) \((x - 6), (x + 3)\)</mcq-correct>
<mcq-option>(B) \((x + 6), (x - 3)\)</mcq-option>
<mcq-option>(C) \((x - 9), (x + 2)\)</mcq-option>
<mcq-option>(D) \((x + 9), (x - 2)\)</mcq-option>
</answer>

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