Question

find the factors of the above quadratic equation.

\\x^2 + 11x - 1452 = 0\\

a. \\((x - 44)(x - 33)\\)
b. \\((x + 44)(x + 33)\\)
c. \\((x - 44)(x + 33)\\)
d. \\((x + 44)(x - 33)\\)

Explanation:

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<reasoning>

Identify the quadratic equation

Using the Quadratic Equations knowledge point
\[
x^2 + 11x - 1452 = 0
\]

Find two numbers that multiply to -1452 and add to 11

Using the Factoring Quadratic Trinomials knowledge point
\[

$$\begin{aligned} &a \cdot b = -1452 \\ &a + b = 11 \\ &44 \cdot (-33) = -1452 \\ &44 + (-33) = 11 \end{aligned}$$

\]

Write the factored form

Using the Factoring Quadratic Trinomials knowledge point
\[
(x + 44)(x - 33) = 0
\]
</reasoning>

<answer>
<mcq-option>a. (x - 44) (x - 33)</mcq-option>
<mcq-option>b. (x + 44) (x + 33)</mcq-option>
<mcq-option>c. (x - 44) (x + 33)</mcq-option>
<mcq-correct>d. (x + 44) (x - 33)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
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"Algebra",
"Factoring Quadratic Trinomials"
]
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Answer:

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<reasoning>

Identify the quadratic equation

Using the Quadratic Equations knowledge point
\[
x^2 + 11x - 1452 = 0
\]

Find two numbers that multiply to -1452 and add to 11

Using the Factoring Quadratic Trinomials knowledge point
\[

$$\begin{aligned} &a \cdot b = -1452 \\ &a + b = 11 \\ &44 \cdot (-33) = -1452 \\ &44 + (-33) = 11 \end{aligned}$$

\]

Write the factored form

Using the Factoring Quadratic Trinomials knowledge point
\[
(x + 44)(x - 33) = 0
\]
</reasoning>

<answer>
<mcq-option>a. (x - 44) (x - 33)</mcq-option>
<mcq-option>b. (x + 44) (x + 33)</mcq-option>
<mcq-option>c. (x - 44) (x + 33)</mcq-option>
<mcq-correct>d. (x + 44) (x - 33)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Quadratic Trinomials"
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