current objective
factor a trinomial using the ac method

question

factor: (20c^2 - 33c + 10).

provide your answer below:

Question

current objective
factor a trinomial using the ac method

question

factor: (20c^2 - 33c + 10).

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 Four Terms" ], "new_concepts": [ "AC Method" ], "current_concepts": [ "Factoring Trinomials", "Factoring by Grouping Four Terms", "AC Method" ] } ## Identify the coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &20c^2 - 33c + 10\ &a = 20,\quad b = -33,\quad c = 10 \end{aligned} $$ ## Find factors of ac that sum to b Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a \cdot c = 20 \cdot 10 = 200\ &b = -33\ &\text{Factors: } -25 \text{ and } -8\ &(-25) \cdot (-8) = 200\ &(-25) + (-8) = -33 \end{aligned} $$ ## Rewrite the middle term Using the *Factoring Trinomials* knowledge point $$ 20c^2 - 25c - 8c + 10 $$ ## Factor by grouping Using the *Factoring by Grouping Four Terms* knowledge point $$ \begin{aligned} &(20c^2 - 25c) - (8c - 10)\ &5c(4c - 5) - 2(4c - 5)\ &(5c - 2)(4c - 5) \end{aligned} $$ $(5c - 2)(4c - 5)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Find factors of ac that sum to b

Rewrite the middle term

Factor by grouping

Answer: