the binomial $(y - 2)$ is a factor of $y^2 - 10y + 16$. what is the other factor?

$(y - 5)$
$(y + 5)$
$(y - 8)$
$(y + 8)$

Question

the binomial $(y - 2)$ is a factor of $y^2 - 10y + 16$. what is the other factor?

$(y - 5)$
$(y + 5)$
$(y - 8)$
$(y + 8)$

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" ] } ## Identify the given polynomial and known factor $$ \begin{aligned} P(y) &= y^2 - 10y + 16 \ F_1(y) &= y - 2 \end{aligned} $$ ## Find the other factor by division or factoring $$ \begin{aligned} y^2 - 10y + 16 &= (y - 2)(y - k) \ 16 &= (-2)(-k) \implies k = 8 \ -10 &= -2 - k \implies -10 = -10 \ F_2(y) &= y - 8 \end{aligned} $$ ## Match with the given options $$ \text{The other factor is } (y - 8). $$

(y - 5)

(y + 5)

(y - 8)

(y + 8)

{ "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

Match with the given options

Answer: