Question

what is the factored form of the polynomial?

(x^2 - 12x + 27)?

( ) ((x + 4)(x + 3))
( ) ((x - 4)(x + 3))
( ) ((x + 9)(x + 3))
( ) ((x - 9)(x - 3))

Explanation:

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<reasoning>

Identify the coefficients of the quadratic trinomial

\[
a = 1, \quad b = -12, \quad c = 27
\]

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

\[

$$\begin{aligned} &p \cdot q = 27\\ &p + q = -12\\ &\Rightarrow p = -9, \quad q = -3 \end{aligned}$$

\]

Write the trinomial in its factored form

\[
x^2 - 12x + 27 = (x - 9)(x - 3)
\]
</reasoning>

<answer>
<mcq-option>(A) \((x + 4)(x + 3)\)</mcq-option>
<mcq-option>(B) \((x - 4)(x + 3)\)</mcq-option>
<mcq-option>(C) \((x + 9)(x + 3)\)</mcq-option>
<mcq-correct>(D) \((x - 9)(x - 3)\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify the coefficients of the quadratic trinomial

\[
a = 1, \quad b = -12, \quad c = 27
\]

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

\[

$$\begin{aligned} &p \cdot q = 27\\ &p + q = -12\\ &\Rightarrow p = -9, \quad q = -3 \end{aligned}$$

\]

Write the trinomial in its factored form

\[
x^2 - 12x + 27 = (x - 9)(x - 3)
\]
</reasoning>

<answer>
<mcq-option>(A) \((x + 4)(x + 3)\)</mcq-option>
<mcq-option>(B) \((x - 4)(x + 3)\)</mcq-option>
<mcq-option>(C) \((x + 9)(x + 3)\)</mcq-option>
<mcq-correct>(D) \((x - 9)(x - 3)\)</mcq-correct>
</answer>

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