11.1 factor the polynomial $2xy + 4x^3y - 12x^5y^4$

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials", "Greatest Common Factor" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials", "Greatest Common Factor" ] } ## Identify the terms of the polynomial We list the three individual terms of the given expression: $$ 2xy,\quad 4x^3y,\quad -12x^5y^4 $$ ## Find the GCF of the coefficients Using the **Greatest Common Factor** knowledge point $$ \text{GCF}(2, 4, 12) = 2 $$ ## Find the GCF of the variable parts Using the **Greatest Common Factor** knowledge point $$ \begin{aligned} &\text{GCF}(x, x^3, x^5) = x\ &\text{GCF}(y, y, y^4) = y\ &\text{GCF of variables} = xy \end{aligned} $$ ## Combine to find the overall GCF Using the **Greatest Common Factor** knowledge point $$ \text{Overall GCF} = 2xy $$ ## Factor out the GCF from each term Using the **Factoring Polynomials** knowledge point $$ \begin{aligned} &2xy = 2xy(1)\ &4x^3y = 2xy(2x^2)\ &-12x^5y^4 = 2xy(-6x^4y^3)\ &2xy + 4x^3y - 12x^5y^4 = 2xy(1 + 2x^2 - 6x^4y^3) \end{aligned} $$ $2xy(1 + 2x^2 - 6x^4y^3)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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Explanation:

Identify the terms of the polynomial

Find the GCF of the coefficients

Find the GCF of the variable parts

Combine to find the overall GCF

Factor out the GCF from each term

Answer: