if one factor of $x^2 + 2x - 24$ is $(x+6)$, what is the other factor?

$(x+8)$
$(x-8)$
$(x+4)$
$(x-4)$

Question

if one factor of $x^2 + 2x - 24$ is $(x+6)$, what is the other factor?

$(x+8)$
$(x-8)$
$(x+4)$
$(x-4)$

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 Division" ] } ## Set up the factoring equation $$ x^2 + 2x - 24 = (x + 6)(x + a) $$ ## Solve for the unknown constant $$ \begin{aligned} 6 \cdot a &= -24 \ a &= -4 \end{aligned} $$ ## Write the other factor $$ (x - 4) $$

(A) $(x+8)$

(B) $(x-8)$

(C) $(x+4)$

(D) $(x-4)$

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

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QUESTION IMAGE

Question

Explanation:

Set up the factoring equation

Solve for the unknown constant

Write the other factor

Answer: