7.4 factoring polynomials using greatest common

what is the gcf of $20x^3$ and $30x^2$?

$5x^2$
$20x^2$
$10x^2$
$10x$

Question

7.4 factoring polynomials using greatest common

what is the gcf of $20x^3$ and $30x^2$?

$5x^2$
$20x^2$
$10x^2$
$10x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Factoring Polynomials" ] } ## Find the GCF of the coefficients Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Factors of } 20: 1, 2, 4, 5, 10, 20\ &\text{Factors of } 30: 1, 2, 3, 5, 6, 10, 15, 30\ &\text{GCF}(20, 30) = 10 \end{aligned} $$ ## Find the GCF of the variable parts Using the *Greatest Common Factor* knowledge point $$ \begin{aligned} &\text{Variable terms: } x^3 \text{ and } x^2\ &\text{GCF}(x^3, x^2) = x^{\min(3, 2)} = x^2 \end{aligned} $$ ## Combine the GCF components Using the *Greatest Common Factor* knowledge point $$ \text{GCF}(20x^3, 30x^2) = 10 \cdot x^2 = 10x^2 $$

(A) $5x^2$

(B) $20x^2$

(C) $10x^2$

(D) $10x$

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

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QUESTION IMAGE

Question

Explanation:

Find the GCF of the coefficients

Find the GCF of the variable parts

Combine the GCF components

Answer: