3. factor the trinomial $10x^2 + 11x - 6$. which of the following is a factor?

$(2x - 3)$

$(5x - 2)$

$(2x - 2)$

$(5x + 3)$

Question

3. factor the trinomial $10x^2 + 11x - 6$. which of the following is a factor?

$(2x - 3)$

$(5x - 2)$

$(2x - 2)$

$(5x + 3)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "AC Method" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "AC Method" ] } ## Identify coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 10x^2 + 11x - 6\ &a = 10,\quad b = 11,\quad c = -6 \end{aligned} $$ ## Apply the AC method Using the *AC Method* knowledge point $$ \begin{aligned} &a \cdot c = 10 \cdot (-6) = -60\ &p \cdot q = -60,\quad p + q = 11 \implies p = 15,\quad q = -4 \end{aligned} $$ ## Rewrite and factor by grouping Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} 10x^2 + 11x - 6 &= 10x^2 + 15x - 4x - 6\ &= 5x(2x + 3) - 2(2x + 3)\ &= (5x - 2)(2x + 3) \end{aligned} $$ ## Identify the matching factor Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} &\text{Factors: } (5x - 2) \text{ and } (2x + 3)\ &\text{Matching option: } (5x - 2) \end{aligned} $$

(A) $(2x - 3)$

(B) $(5x - 2)$

(C) $(2x - 2)$

(D) $(5x + 3)$

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

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QUESTION IMAGE

Question

Explanation:

Identify coefficients

Apply the AC method

Rewrite and factor by grouping

Identify the matching factor

Answer: