if $x - 9$ is a factor of $x^2 - 5x - 36$, what is the other factor?

$x - 4$
$x + 4$
$x - 6$
$x + 6$

Question

if $x - 9$ is a factor of $x^2 - 5x - 36$, what is the other factor?

$x - 4$
$x + 4$
$x - 6$
$x + 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Factoring Trinomials", "Polynomial Division" ], "current_concepts": [ "Factoring Trinomials", "Polynomial Division" ] } ## Identify the given polynomial and known factor $$ \begin{aligned} P(x) &= x^2 - 5x - 36 \ F_1(x) &= x - 9 \end{aligned} $$ ## Find the other factor by division or factoring $$ \begin{aligned} x^2 - 5x - 36 &= (x - 9)(x + a) \ -9 \cdot a &= -36 \implies a = 4 \ x^2 - 5x - 36 &= (x - 9)(x + 4) \end{aligned} $$ ## Select the matching option $$ F_2(x) = x + 4 $$

$x - 4$

$x + 4$

$x - 6$

$x + 6$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given polynomial and known factor

Find the other factor by division or factoring

Select the matching option

Answer: