factoring the gcf from a polynomial

what is the factored form of the polynomial $27x^2y - 43xy^2$?

$xy(27x - 43y)$
$x^2y^2(27 - 43)$
$3xy(9x - 17y)$
$3x^2y(9 - 14y)$

Question

factoring the gcf from a polynomial

what is the factored form of the polynomial $27x^2y - 43xy^2$?

$xy(27x - 43y)$
$x^2y^2(27 - 43)$
$3xy(9x - 17y)$
$3x^2y(9 - 14y)$

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", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor of Monomials", "Factoring Polynomials" ] } ## Find the GCF of the coefficients $$ \gcd(27, 43) = 1 $$ ## Find the GCF of the variable parts $$ \gcd(x^2y, xy^2) = xy $$ ## Factor out the GCF from the polynomial $$ 27x^2y - 43xy^2 = xy(27x - 43y) $$

(A) $xy(27x - 43y)$

(B) $x^2y^2(27 - 43)$

(C) $3xy(9x - 17y)$

(D) $3x^2y(9 - 14y)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Find the GCF of the coefficients

Find the GCF of the variable parts

Factor out the GCF from the polynomial

Answer: