Question

what are the factors of (6x^2+37x-60)?

(3x-4) and (2x+15)
(3x+4) and (2x-15)
(2(x-2)) and (3(x+5))
(2(x+2)) and (3(x-5))

Explanation:

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<reasoning>

Identify the quadratic expression

\[
6x^2 + 37x - 60
\]

Find factors by testing the given options

\[

$$\begin{aligned} (3x - 4)(2x + 15) &= 3x(2x + 15) - 4(2x + 15) \\ &= 6x^2 + 45x - 8x - 60 \\ &= 6x^2 + 37x - 60 \end{aligned}$$

\]

Verify other options

\[

$$\begin{aligned} (3x + 4)(2x - 15) &= 6x^2 - 45x + 8x - 60 = 6x^2 - 37x - 60 \\ 2(x - 2) \cdot 3(x + 5) &= 6(x^2 + 3x - 10) = 6x^2 + 18x - 60 \\ 2(x + 2) \cdot 3(x - 5) &= 6(x^2 - 3x - 10) = 6x^2 - 18x - 60 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(3x-4\) and \(2x+15\)</mcq-correct>
<mcq-option>(B) \(3x+4\) and \(2x-15\)</mcq-option>
<mcq-option>(C) \(2(x-2)\) and \(3(x+5)\)</mcq-option>
<mcq-option>(D) \(2(x+2)\) and \(3(x-5)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the quadratic expression

\[
6x^2 + 37x - 60
\]

Find factors by testing the given options

\[

$$\begin{aligned} (3x - 4)(2x + 15) &= 3x(2x + 15) - 4(2x + 15) \\ &= 6x^2 + 45x - 8x - 60 \\ &= 6x^2 + 37x - 60 \end{aligned}$$

\]

Verify other options

\[

$$\begin{aligned} (3x + 4)(2x - 15) &= 6x^2 - 45x + 8x - 60 = 6x^2 - 37x - 60 \\ 2(x - 2) \cdot 3(x + 5) &= 6(x^2 + 3x - 10) = 6x^2 + 18x - 60 \\ 2(x + 2) \cdot 3(x - 5) &= 6(x^2 - 3x - 10) = 6x^2 - 18x - 60 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(3x-4\) and \(2x+15\)</mcq-correct>
<mcq-option>(B) \(3x+4\) and \(2x-15\)</mcq-option>
<mcq-option>(C) \(2(x-2)\) and \(3(x+5)\)</mcq-option>
<mcq-option>(D) \(2(x+2)\) and \(3(x-5)\)</mcq-option>
</answer>

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