the trinomial (2x^2 + 13x + 6) has a linear factor of (x + 6).
(2x^2 + 13x + 6 = (x + 6)(?))
what is the other linear factor?

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

Question

the trinomial (2x^2 + 13x + 6) has a linear factor of (x + 6).
(2x^2 + 13x + 6 = (x + 6)(?))
what is the other linear factor?

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials", "Polynomial Division" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials", "Polynomial Division", "Algebra Tiles" ] } ## Set up the polynomial equation $$ 2x^2 + 13x + 6 = (x + 6)(ax + b) $$ ## Solve for the coefficients $$ \begin{aligned} a &= \frac{2x^2}{x} = 2x \ b &= \frac{6}{6} = 1 \end{aligned} $$ ## Verify the middle term $$ (x + 6)(2x + 1) = 2x^2 + x + 12x + 6 = 2x^2 + 13x + 6 $$

(A) $x + 3$

(B) $x + 6$

(C) $2x + 1$

(D) $2x + 3$

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

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QUESTION IMAGE

Question

Explanation:

Set up the polynomial equation

Solve for the coefficients

Verify the middle term

Answer: