which expression is a factor of (10x^2 + 11x + 3)?

* (x - 3)
* (2x + 1)
* (5x - 3)
* (10x + 3)

Question

which expression is a factor of (10x^2 + 11x + 3)?

* (x - 3)
* (2x + 1)
* (5x - 3)
* (10x + 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" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Polynomial Operations" ] } ## Identify the coefficients of the quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a = 10\ &b = 11\ &c = 3 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a \cdot c = 10 \cdot 3 = 30\ &p \cdot q = 30,\quad p + q = 11\ &p = 5,\quad q = 6 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} 10x^2 + 11x + 3 &= 10x^2 + 5x + 6x + 3\ &= 5x(2x + 1) + 3(2x + 1)\ &= (2x + 1)(5x + 3) \end{aligned} $$ ## Compare the factors with the given options Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &\text{Factors: } (2x + 1), (5x + 3)\ &\text{Matching option: } 2x + 1 \end{aligned} $$

(A) $x - 3$

(B) $2x + 1$

(C) $5x - 3$

(D) $10x + 3$

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic trinomial

Find two numbers that multiply to ac and add to b

Rewrite the middle term and factor by grouping

Compare the factors with the given options

Answer: