select the correct answer.

which expression is equivalent to this polynomial?

(15x - 24)

(3(5x - 8))
(3(5x - 5))
(5(3x - 8))
(3(5x - 24))

Question

select the correct answer.

which expression is equivalent to this polynomial?

(15x - 24)

(3(5x - 8))
(3(5x - 5))
(5(3x - 8))
(3(5x - 24))

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property" ], "new_concepts": [ "Greatest Common Factor", "Factoring Polynomials" ], "current_concepts": [ "Distributive Property", "Greatest Common Factor", "Factoring Polynomials" ] } ## Find the greatest common factor $$ \begin{aligned} &\text{Terms: } 15x, \quad -24 \ &\text{Factors of } 15: 1, 3, 5, 15 \ &\text{Factors of } 24: 1, 2, 3, 4, 6, 8, 12, 24 \ &\text{GCF}(15, 24) = 3 \end{aligned} $$ ## Factor out the greatest common factor $$ \begin{aligned} 15x - 24 &= 3 \cdot 5x - 3 \cdot 8 \ &= 3(5x - 8) \end{aligned} $$ ## Verify the options $$ \begin{aligned} &3(5x - 8) = 15x - 24 \quad (\text{Correct}) \ &3(5x - 5) = 15x - 15 \ &5(3x - 8) = 15x - 40 \ &3(5x - 24) = 15x - 72 \end{aligned} $$

(A) $3(5x - 8)$

(B) $3(5x - 5)$

(C) $5(3x - 8)$

(D) $3(5x - 24)$

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

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QUESTION IMAGE

Question

Explanation:

Find the greatest common factor

Factor out the greatest common factor

Verify the options

Answer: