what are the factors of (6x^2+37x-60)?

(3x-4) and (2x+15)
(3x+4) and (2x-15)
(2(x-2)) and (3(x+5))
(2(x+2)) and (3(x-5))

Question

what are the factors of (6x^2+37x-60)?

(3x-4) and (2x+15)
(3x+4) and (2x-15)
(2(x-2)) and (3(x+5))
(2(x+2)) and (3(x-5))

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", "Polynomial Multiplication" ] } ## Identify the quadratic expression $$ 6x^2 + 37x - 60 $$ ## Find factors by testing the given options $$ \begin{aligned} (3x - 4)(2x + 15) &= 3x(2x + 15) - 4(2x + 15) \ &= 6x^2 + 45x - 8x - 60 \ &= 6x^2 + 37x - 60 \end{aligned} $$ ## Verify other options $$ \begin{aligned} (3x + 4)(2x - 15) &= 6x^2 - 45x + 8x - 60 = 6x^2 - 37x - 60 \ 2(x - 2) \cdot 3(x + 5) &= 6(x^2 + 3x - 10) = 6x^2 + 18x - 60 \ 2(x + 2) \cdot 3(x - 5) &= 6(x^2 - 3x - 10) = 6x^2 - 18x - 60 \end{aligned} $$

(A) $3x-4$ and $2x+15$

(B) $3x+4$ and $2x-15$

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

(D) $2(x+2)$ and $3(x-5)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the quadratic expression

Find factors by testing the given options

Verify other options

Answer: