the polynomial $6x^2 + x - 15$ has a factor of $2x - 3$. what is the other factor?

$3x - 5$
$3x + 5$
$4x - 5$
$4x + 5$

Question

the polynomial $6x^2 + x - 15$ has a factor of $2x - 3$. what is the other factor?

$3x - 5$
$3x + 5$
$4x - 5$
$4x + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials", "Polynomial Division" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials", "Polynomial Division" ] } ## Set up the factoring equation $$ 6x^2 + x - 15 = (2x - 3)(ax + b) $$ ## Determine the coefficients $$ \begin{aligned} 2a &= 6 \implies a = 3 \ -3b &= -15 \implies b = 5 \end{aligned} $$ ## Verify the middle term $$ (2x - 3)(3x + 5) = 6x^2 + 10x - 9x - 15 = 6x^2 + x - 15 $$

(A) $3x - 5$

(B) $3x + 5$

(C) $4x - 5$

(D) $4x + 5$

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

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Question

Explanation:

Set up the factoring equation

Determine the coefficients

Verify the middle term

Answer: