what is the factorization of (3x^2 - 8x + 5)?

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

Question

what is the factorization of (3x^2 - 8x + 5)?

(3x - 1)(x + 5)
(3x + 5)(x - 1)
(3x - 1)(x - 5)
(3x - 5)(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" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Trinomial Coefficients" ] } ## Identify the coefficients of the quadratic trinomial $$ a = 3, \quad b = -8, \quad c = 5 $$ ## Find two numbers that multiply to $ac$ and add to $b$ $$ \begin{aligned} &ac = 3 \times 5 = 15\ &b = -8\ &\text{The two numbers are } -3 \text{ and } -5 \text{ since:}\ &(-3) \times (-5) = 15\ &(-3) + (-5) = -8 \end{aligned} $$ ## Rewrite and factor the trinomial by grouping $$ \begin{aligned} 3x^2 - 8x + 5 &= 3x^2 - 3x - 5x + 5\ &= 3x(x - 1) - 5(x - 1)\ &= (3x - 5)(x - 1) \end{aligned} $$

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

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

(C) $(3x - 1)(x - 5)$

(D) $(3x - 5)(x - 1)$

{ "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 and factor the trinomial by grouping

Answer: