Question

modeling the factored form of a trinomial

what side lengths should be used to model a rectangle with an area of \\(x^2 + 3x - 10\\) square units?

\\(x - 5\\) and \\(x + 2\\)
\\(x - 2\\) and \\(x + 5\\)
\\(x\\) and \\(x + 3\\)
\\(x + 3\\) and \\(x - 10\\)

Explanation:

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<reasoning>

Identify the given area and target side lengths

Using the Area Model Multiplication knowledge point
\[
\text{Area} = x^2 + 3x - 10
\]
\[
\text{Area} = \text{Factor 1} \times \text{Factor 2}
\]

Factor the trinomial expression

Using the Factoring Trinomials knowledge point
\[
x^2 + 3x - 10 = (x - 2)(x + 5)
\]

Match with the given options

Using the Factoring Trinomials knowledge point
\[
\text{Side lengths} = x - 2 \text{ and } x + 5
\]
</reasoning>

<answer>
<mcq-option>(A) \(x - 5\) and \(x + 2\)</mcq-option>
<mcq-correct>(B) \(x - 2\) and \(x + 5\)</mcq-correct>
<mcq-option>(C) \(x\) and \(x + 3\)</mcq-option>
<mcq-option>(D) \(x + 3\) and \(x - 10\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given area and target side lengths

Using the Area Model Multiplication knowledge point
\[
\text{Area} = x^2 + 3x - 10
\]
\[
\text{Area} = \text{Factor 1} \times \text{Factor 2}
\]

Factor the trinomial expression

Using the Factoring Trinomials knowledge point
\[
x^2 + 3x - 10 = (x - 2)(x + 5)
\]

Match with the given options

Using the Factoring Trinomials knowledge point
\[
\text{Side lengths} = x - 2 \text{ and } x + 5
\]
</reasoning>

<answer>
<mcq-option>(A) \(x - 5\) and \(x + 2\)</mcq-option>
<mcq-correct>(B) \(x - 2\) and \(x + 5\)</mcq-correct>
<mcq-option>(C) \(x\) and \(x + 3\)</mcq-option>
<mcq-option>(D) \(x + 3\) and \(x - 10\)</mcq-option>
</answer>

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