practice factoring trinomials with a leading coefficient of 1 and a positive constant term.

the binomial $(x + 5)$ is a factor of $x^2 + 8x + 15$. what is the other factor?

$(x + 3)$
$(x + 7)$
$(x + 12)$
$(x + 13)$

Question

practice factoring trinomials with a leading coefficient of 1 and a positive constant term.

the binomial $(x + 5)$ is a factor of $x^2 + 8x + 15$. what is the other factor?

$(x + 3)$
$(x + 7)$
$(x + 12)$
$(x + 13)$

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 $$ \begin{aligned} P(x) &= x^2 + 8x + 15 \ F_1(x) &= x + 5 \end{aligned} $$ ## Find the other factor by division or factorization $$ \begin{aligned} x^2 + 8x + 15 &= (x + 5)(x + a) \ x^2 + 8x + 15 &= x^2 + (5 + a)x + 5a \ 5a &= 15 \implies a = 3 \ F_2(x) &= x + 3 \end{aligned} $$ ## Match with the given options $$ \text{The other factor is } (x + 3). $$

(x + 3)

(x + 7)

(x + 12)

(x + 13)

{ "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 factorization

Match with the given options

Answer: