which is the correct factorization of (6x^2+17x+5)?

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

Question

which is the correct factorization of (6x^2+17x+5)?

(3x+1)(2x+5)
(3x-1)(2x+5)
(2x+1)(3x-3)
(2x-1)(3x+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 Polynomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials" ] } ## Identify the coefficients of the quadratic expression Using the *Factoring Polynomials* knowledge point $$ \begin{aligned} &ax^2 + bx + c = 6x^2 + 17x + 5\ &a = 6,\quad b = 17,\quad c = 5 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Factoring Polynomials* knowledge point $$ \begin{aligned} &ac = 6 \times 5 = 30\ &p \times q = 30,\quad p + q = 17\ &p = 15,\quad q = 2 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Factoring Polynomials* knowledge point $$ \begin{aligned} &6x^2 + 15x + 2x + 5\ &= 3x(2x + 5) + 1(2x + 5)\ &= (3x + 1)(2x + 5) \end{aligned} $$

(A) $(3x+1)(2x+5)$

(B) $(3x-1)(2x+5)$

(C) $(2x+1)(3x-3)$

(D) $(2x-1)(3x+3)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic expression

Find two numbers that multiply to ac and add to b

Rewrite the middle term and factor by grouping

Answer: