identifying the common factors in a polynomial

factor $26r^3s + 52r^5 - 39r^2s^4$. what is the resulting expression?

$13(2r^3s + 4r^5 - 3r^2s^4)$
$13r^2s(2r + 4r^3 - 3s^3)$
$13r^2(2rs + 4r^3 - 3s^4)$
$13r^2(26r^3s + 52r^5 - 39r^2s^4)$

Question

identifying the common factors in a polynomial

factor $26r^3s + 52r^5 - 39r^2s^4$. what is the resulting expression?

$13(2r^3s + 4r^5 - 3r^2s^4)$
$13r^2s(2r + 4r^3 - 3s^3)$
$13r^2(2rs + 4r^3 - 3s^4)$
$13r^2(26r^3s + 52r^5 - 39r^2s^4)$

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 greatest common factor of the coefficients $$ \text{gcd}(26, 52, 39) = 13 $$ ## Find the greatest common factor of the variable parts $$ \begin{aligned} &\text{For } r: \min(3, 1, 2) = 1 \implies r^1 \ &\text{For } s: \min(1, 5, 4) = 1 \implies s^1 \ &\text{GCF of variable parts} = rs \end{aligned} $$ ## Divide each term by the GCF to find the remaining expression $$ \begin{aligned} &\text{Overall GCF} = 13rs \ &\frac{26r^3s}{13rs} = 2r^2 \ &\frac{52rs^5}{13rs} = 4s^4 \ &\frac{-39r^2s^4}{13rs} = -3rs^3 \ &\text{Factored expression} = 13rs(2r^2 + 4s^4 - 3rs^3) \end{aligned} $$

(A) $13(2r^3s + 4rs^5 - 3r^2s^4)$

(B) $13r^2s(2r + 4r^3 - 3s^3)$

(C) $13rs(2r^2 + 4s^4 - 3rs^3)$

(D) $13r^2(26r^3s + 52rs^5 - 3r^2s^4)$

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

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QUESTION IMAGE

Question

Explanation:

Find the greatest common factor of the coefficients

Find the greatest common factor of the variable parts

Divide each term by the GCF to find the remaining expression

Answer: