factoring polynomials: gcf
finding the gcf of two monomials
what is the gcf of $48m^5n$ and $81m^2n^2$?
- $3mn$
- $3m^2n$
- $48m^2n$
- $129m^5n^2$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor of Monomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor of Monomials" ] } ## Find the GCF of the numerical coefficients $$ \begin{aligned} &48 = 2^4 \times 3\ &81 = 3^4\ &\text{GCF}(48, 81) = 3^1 = 3 \end{aligned} $$ ## Find the GCF of the variable parts $$ \begin{aligned} &\text{GCF}(m^5, m^2) = m^{\min(5, 2)} = m^2\ &\text{GCF}(n^1, n^2) = n^{\min(1, 2)} = n^1 = n \end{aligned} $$ ## Combine the numerical and variable GCFs $$ \text{GCF}(48m^5n, 81m^2n^2) = 3 \times m^2 \times n = 3m^2n $$

(A) $3mn$

(B) $3m^2n$

(C) $48m^2n$

(D) $129m^5n^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Greatest Common Factor of Monomials" ] }

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QUESTION IMAGE

Question

Explanation:

Find the GCF of the numerical coefficients

Find the GCF of the variable parts

Combine the numerical and variable GCFs

Answer: