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

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

Question

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

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

Accepted Answer

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

(A) $x - 8$

(B) $2x - 1$

(C) $3x + 8$

(D) $4x + 1$

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

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QUESTION IMAGE

Question

Explanation:

Identify coefficients

Find factors of ac that sum to b

Factor by grouping

Answer: