current objective
factor a trinomial using the ac method

question
factor: (10q^2 + 33q + 20).

provide your answer below:

Question

current objective
factor a trinomial using the ac method

question
factor: (10q^2 + 33q + 20).

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Factoring by Grouping" ] } ## Identify coefficients of the trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &10q^2 + 33q + 20\ &a = 10,\quad b = 33,\quad c = 20 \end{aligned} $$ ## Find two numbers that multiply to ac and add to b Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a \cdot c = 10 \cdot 20 = 200\ &p \cdot r = 200,\quad p + r = 33\ &p = 25,\quad r = 8 \end{aligned} $$ ## Rewrite the middle term and factor by grouping Using the *Factoring by Grouping* knowledge point $$ \begin{aligned} &10q^2 + 25q + 8q + 20\ &5q(2q + 5) + 4(2q + 5)\ &(5q + 4)(2q + 5) \end{aligned} $$ $(5q + 4)(2q + 5)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the trinomial

Find two numbers that multiply to ac and add to b

Rewrite the middle term and factor by grouping

Answer: