1. factor the trinomial: $2x^2 + 7x + 3$. which of the following is a factor?

$(2x + 1)$

$(2x - 1)$

$(x - 3)$

$(2x + 3)$

Question

1. factor the trinomial: $2x^2 + 7x + 3$. which of the following is a factor?

$(2x + 1)$

$(2x - 1)$

$(x - 3)$

$(2x + 3)$

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": [ "Algebraic Simplification" ], "new_concepts": [ "Factoring Trinomials", "AC Method" ], "current_concepts": [ "Algebraic Simplification", "Factoring Trinomials", "AC Method" ] } ## Identify the coefficients Using the **Algebraic Simplification** knowledge point $$ \begin{aligned} &a = 2\ &b = 7\ &c = 3 \end{aligned} $$ ## Find factors for grouping Find two numbers that multiply to $a \cdot c = 6$ and add to $b = 7$. These numbers are $6$ and $1$. ## Rewrite and factor by grouping Rewrite the middle term and group: $$ \begin{aligned} 2x^2 + 7x + 3 &= 2x^2 + 6x + x + 3\ &= 2x(x + 3) + 1(x + 3)\ &= (2x + 1)(x + 3) \end{aligned} $$ ## Identify the matching factor Compare the factors $(2x + 1)$ and $(x + 3)$ with the given options. The factor $(2x + 1)$ matches the first option.

(2x + 1)

(2x - 1)

(x - 3)

(2x + 3)

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Find factors for grouping

Rewrite and factor by grouping

Identify the matching factor

Answer: