$4x^2$ is the gcf of this polynomial.

$20x^2y + 56x^3 - ?$

which could be the mystery term?

* $22x^3$
* $24x^2y$
* $26x^2y$
* $28y^3$

Question

$4x^2$ is the gcf of this polynomial.

$20x^2y + 56x^3 - ?$

which could be the mystery term?

* $22x^3$
* $24x^2y$
* $26x^2y$
* $28y^3$

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 of Monomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor of Monomials", "Factoring Polynomials" ] } ## Analyze the given terms Using the *Greatest Common Factor of Monomials* knowledge point $$ \begin{aligned} &20x^2y = 4 \cdot 5 \cdot x^2 \cdot y = (4x^2) \cdot (5y)\ &56x^3 = 4 \cdot 14 \cdot x^2 \cdot x = (4x^2) \cdot (14x) \end{aligned} $$ ## Evaluate the options for the mystery term Using the *Greatest Common Factor of Monomials* knowledge point $$ \begin{aligned} &\text{Option 1: } 22x^3 = 2 \cdot 11 \cdot x^3 \implies \gcd(20x^2y, 56x^3, 22x^3) = 2x^2 e 4x^2\ &\text{Option 2: } 24x^2y = 4 \cdot 6 \cdot x^2 \cdot y \implies \gcd(20x^2y, 56x^3, 24x^2y) = 4x^2\ &\text{Option 3: } 26x^2y = 2 \cdot 13 \cdot x^2 \cdot y \implies \gcd(20x^2y, 56x^3, 26x^2y) = 2x^2 e 4x^2\ &\text{Option 4: } 28y^3 = 4 \cdot 7 \cdot y^3 \implies \gcd(20x^2y, 56x^3, 28y^3) = 4 e 4x^2 \end{aligned} $$ ## Confirm the correct mystery term Using the *Greatest Common Factor of Monomials* knowledge point $$ \begin{aligned} &\gcd(20, 56, 24) = 4\ &\gcd(x^2, x^3, x^2) = x^2\ &\gcd(y, 1, y) = 1\ &\text{GCF} = 4x^2 \end{aligned} $$

(A) $22x^3$

(B) $24x^2y$

(C) $26x^2y$

(D) $28y^3$

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

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QUESTION IMAGE

Question

Explanation:

Analyze the given terms

Evaluate the options for the mystery term

Confirm the correct mystery term

Answer: