what is the factored form of the polynomial?

(x^2 + 9x + 20)

- ((x - 4)(x - 5))
- ((x - 2)(x - 10))
- ((x + 4)(x + 5))
- ((x + 2)(x + 10))

Question

what is the factored form of the polynomial?

(x^2 + 9x + 20)

- ((x - 4)(x - 5))
- ((x - 2)(x - 10))
- ((x + 4)(x + 5))
- ((x + 2)(x + 10))

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", "X Method Factoring" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "X Method Factoring" ] } ## Identify the coefficients of the quadratic trinomial $$ \begin{aligned} &x^2 + 9x + 20\ &a = 1,\quad b = 9,\quad c = 20 \end{aligned} $$ ## Find two numbers that multiply to c and add to b $$ \begin{aligned} &p \cdot q = 20\ &p + q = 9\ &\text{Factors of } 20: (1, 20), (2, 10), (4, 5)\ &4 + 5 = 9 \implies p = 4,\quad q = 5 \end{aligned} $$ ## Write the trinomial in its factored form $$ x^2 + 9x + 20 = (x + 4)(x + 5) $$

(A) $(x - 4)(x - 5)$

(B) $(x - 2)(x - 10)$

(C) $(x + 4)(x + 5)$

(D) $(x + 2)(x + 10)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic trinomial

Find two numbers that multiply to c and add to b

Write the trinomial in its factored form

Answer: