select the correct answer.

which expression shows the factors of (5x^2 + 17x + 6)?

(5x + 1)(x + 6)
(5x + 2)(x + 3)
(5x + 3)(x + 2)
(5x + 6)(x + 1)

Question

select the correct answer.

which expression shows the factors of (5x^2 + 17x + 6)?

(5x + 1)(x + 6)
(5x + 2)(x + 3)
(5x + 3)(x + 2)
(5x + 6)(x + 1)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Factoring Polynomials" ] } ## Identify coefficients of the quadratic expression $$ a = 5, \quad b = 17, \quad c = 6 $$ ## Find two numbers that multiply to $ac$ and add to $b$ $$ \begin{aligned} &ac = 5 \times 6 = 30\ &p \times q = 30, \quad p + q = 17 \implies p = 15, \quad q = 2 \end{aligned} $$ ## Rewrite and factor by grouping $$ \begin{aligned} 5x^2 + 17x + 6 &= 5x^2 + 15x + 2x + 6\ &= 5x(x + 3) + 2(x + 3)\ &= (5x + 2)(x + 3) \end{aligned} $$

(A) $(5x + 1)(x + 6)$

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

(C) $(5x + 3)(x + 2)$

(D) $(5x + 6)(x + 1)$

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

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic expression

Find two numbers that multiply to \(ac\) and add to \(b\)

Rewrite and factor by grouping

Answer: