completely factor the trinomial, if possible.

\16y^4 + 60y^3 + 36y^2\

Question

completely factor the trinomial, if possible.

\16y^4 + 60y^3 + 36y^2\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials", "Trinomial Factoring by Grouping" ] } ## Factor out the greatest common factor (GCF) Using the *Factoring Polynomials by GCF* knowledge point $$ \begin{aligned} \text{GCF}(16y^4, 60y^3, 36y^2) &= 4y^2 \ 16y^4 + 60y^3 + 36y^2 &= 4y^2(4y^2 + 15y + 9) \end{aligned} $$ ## Find factors for the inner trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &a = 4,\quad b = 15,\quad c = 9 \ &a \cdot c = 36 \ &\text{Factors of } 36 \text{ that sum to } 15: 12 \text{ and } 3 \end{aligned} $$ ## Factor the trinomial by grouping Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} 4y^2 + 15y + 9 &= 4y^2 + 12y + 3y + 9 \ &= 4y(y + 3) + 3(y + 3) \ &= (4y + 3)(y + 3) \end{aligned} $$ ## Write the completely factored expression Using the *Factoring Trinomials* knowledge point $$ 16y^4 + 60y^3 + 36y^2 = 4y^2(4y+3)(y+3) $$ $4y^2(4y+3)(y+3)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor (GCF)

Find factors for the inner trinomial

Factor the trinomial by grouping

Write the completely factored expression

Answer: