7.4 factoring polynomials using greatest common factors quiz

what is the gcf of $12x^2$ and $18x$?

Question

7.4 factoring polynomials using greatest common factors quiz

what is the gcf of $12x^2$ and $18x$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Factoring Polynomials" ] } ## Find the GCF of the numerical coefficients Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &12 = 2^2 \times 3\ &18 = 2 \times 3^2\ &\text{GCF}(12, 18) = 2^1 \times 3^1 = 6 \end{aligned} $$ ## Find the GCF of the variable parts Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Variable terms: } x^2 \text{ and } x^1\ &\text{GCF}(x^2, x) = x^{\min(2, 1)} = x \end{aligned} $$ ## Combine the numerical and variable factors Using the *Factoring Polynomials* knowledge point $$ \text{GCF}(12x^2, 18x) = 6 \times x = 6x $$ What is the GCF of $12x^2$ and $18x$? $6x$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Greatest Common Factor" ] }

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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 factors

Answer: