completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\3z^2 - 23z - 8\

Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\3z^2 - 23z - 8\

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", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Trinomial Factoring by Grouping", "Finding Factors with Given Sum and Product" ] } ## Identify the coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &3z^2 - 23z - 8\ &a = 3,\quad b = -23,\quad c = -8 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &ac = 3 \times (-8) = -24\ &b = -23\ &\text{Factors: } -24 \text{ and } 1\ &-24 \times 1 = -24\ &-24 + 1 = -23 \end{aligned} $$ ## Rewrite and group the terms Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} &3z^2 - 23z - 8 = 3z^2 - 24z + z - 8\ & = (3z^2 - 24z) + (z - 8) \end{aligned} $$ ## Factor out the greatest common factor Using the *Factoring Trinomials* and *Trinomial Factoring by Grouping* knowledge points $$ \begin{aligned} &3z(z - 8) + 1(z - 8)\ & = (3z + 1)(z - 8) \end{aligned} $$ $(3z + 1)(z - 8)$ { "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 with given sum and product

Rewrite and group the terms

Factor out the greatest common factor

Answer: