which expression is a factor of (12x^2 + 29x - 8)? - (x - 8) - (2x - 1) - (3x + 8) - (4x + 1)

which expression is a factor of (12x^2 + 29x - 8)? - (x - 8) - (2x - 1)…

QUESTION IMAGE

Question

which expression is a factor of (12x^2 + 29x - 8)?

(x - 8)
(2x - 1)
(3x + 8)
(4x + 1)

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Factoring Trinomials",
"Trinomial Coefficients"
],
"new_concepts": [],
"current_concepts": [
"Factoring Trinomials",
"Trinomial Coefficients"
]
}
</pre_analysis>

Identify coefficients

\[
a = 12, \quad b = 29, \quad c = -8
\]

Find factors of ac that sum to b

\[

\begin{aligned} &ac = 12 \times (-8) = -96 \\ &32 \times (-3) = -96 \\ &32 + (-3) = 29 \end{aligned}

\]

Factor by grouping

\[

\begin{aligned} 12x^2 + 29x - 8 &= 12x^2 + 32x - 3x - 8 \\ &= 4x(3x + 8) - 1(3x + 8) \\ &= (4x - 1)(3x + 8) \end{aligned}

\]
</reasoning>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factoring Trinomials"
]
}
</post_analysis>

Answer: