solve the equation by factoring.
enter the smallest solution first.
\3x^2 - 5x - 12 = 0\
\x = -\frac{?}{ }, \

Question

solve the equation by factoring.
enter the smallest solution first.
\3x^2 - 5x - 12 = 0\
\x = -\frac{?}{ },  \

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "AC Method", "Factor by Grouping" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "AC Method", "Factor by Grouping", "Polynomial Factoring" ] } ## Identify coefficients Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} &3x^2 - 5x - 12 = 0\ &a = 3,\quad b = -5,\quad c = -12 \end{aligned} $$ ## Find factors for AC method Using the *AC Method* knowledge point $$ \begin{aligned} &a \cdot c = 3 \cdot (-12) = -36\ &\text{Factors of } -36 \text{ that sum to } -5: \quad -9 \text{ and } 4\ &-9 + 4 = -5 \end{aligned} $$ ## Rewrite and factor by grouping Using the *Factor by Grouping* knowledge point $$ \begin{aligned} &3x^2 - 9x + 4x - 12 = 0\ &3x(x - 3) + 4(x - 3) = 0\ &(3x + 4)(x - 3) = 0 \end{aligned} $$ ## Solve for x Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} &3x + 4 = 0 \implies x = -\frac{4}{3}\ &x - 3 = 0 \implies x = 3 \end{aligned} $$ ## Order the solutions Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} &-\frac{4}{3} < 3\ &\text{Smallest solution: } -\frac{4}{3}\ &\text{Largest solution: } 3 \end{aligned} $$ Solve the equation by factoring. Enter the smallest solution first. $3x^2 - 5x - 12 = 0$ $x = -$ $\frac{4}{3}$ , $3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients

Find factors for AC method

Rewrite and factor by grouping

Solve for x

Order the solutions

Answer: