factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial factor) and rewrite the expression.

\5xy^3 + 25x^2y - 10xy\

Question

factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial factor) and rewrite the expression.

\5xy^3 + 25x^2y - 10xy\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Factoring Monomials" ], "new_concepts": [ "Factoring Polynomials by GCF" ], "current_concepts": [ "Greatest Common Factor", "Factoring Monomials", "Factoring Polynomials by GCF" ] } ## Identify the terms of the polynomial Using the **Factoring Monomials** knowledge point The terms of the given polynomial are: $$ \begin{aligned} &\text{Term 1: } 5xy^3 \ &\text{Term 2: } 25x^2y \ &\text{Term 3: } -10xy \end{aligned} $$ ## Find the greatest common factor of the coefficients Using the **Greatest Common Factor** knowledge point $$ \text{gcd}(5, 25, -10) = 5 $$ ## Find the greatest common factor of the variable parts Using the **Factoring Monomials** knowledge point $$ \begin{aligned} &\text{For } x: \min(1, 2, 1) = 1 \implies x^1 \ &\text{For } y: \min(3, 1, 1) = 1 \implies y^1 \ &\text{Variable GCF: } xy \end{aligned} $$ ## Determine the overall greatest common monomial factor Using the **Greatest Common Factor** and **Factoring Monomials** knowledge points $$ \text{GCF} = 5xy $$ ## Divide each term by the GCF to rewrite the expression Using the **Greatest Common Factor** knowledge point $$ \begin{aligned} &\frac{5xy^3}{5xy} = y^2 \ &\frac{25x^2y}{5xy} = 5x \ &\frac{-10xy}{5xy} = -2 \ &5xy^3 + 25x^2y - 10xy = 5xy(y^2 + 5x - 2) \end{aligned} $$ $5xy(y^2 + 5x - 2)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials by GCF" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the terms of the polynomial

Find the greatest common factor of the coefficients

Find the greatest common factor of the variable parts

Determine the overall greatest common monomial factor

Divide each term by the GCF to rewrite the expression

Answer: